11π12=3π4+π611π12=3π4+π6 Find the exact values of the sine, cosine
- MATH
sin(π2−x)=cos(x)sin(π2-x)=cos(x) Prove the identity.
Use the formula for the sine of the sum of angles: sin(a−b)=sin(a)cos(b)−cos(a)sin(b)sin(a-b)=sin(a)cos(b)-cos(a)sin(b) for a=π2a=π2 and b=x.b=x. It gives sin(π2−x)=sin(π2)cos(x)−cos(π2)sin(x).sin(π2-x)=sin(π2)cos(x)-cos(π2)sin(x). Because sin(π2)=1sin(π2)=1 and…
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sec(v−u)sec(v-u) Find the exact value of the trigonometric expression given that sin(u) = -7/25…
Given sin(u)=−725,cos(v)=−45sin(u)=-725,cos(v)=-45 using pythagorean identity, sin2(u)+cos2(u)=1sin2(u)+cos2(u)=1 (−725)2+cos2(u)=1(-725)2+cos2(u)=1 cos2(u)=1−49625=625−49625=576625cos2(u)=1-49625=625-49625=576625 cos(u)=576625−−−−√cos(u)=576625 cos(u)=±2425cos(u)=±2425 since u…
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csc(u−v)csc(u-v) Find the exact value of the trigonometric expression given that sin(u) = -7/25…
Given sin(u)=−725,cos(v)=−45sin(u)=-725,cos(v)=-45 using pythagorean identity, sin2(u)+cos2(u)=1sin2(u)+cos2(u)=1 (−725)2+cos2(u)=1(-725)2+cos2(u)=1 cos2(u)=1−49625cos2(u)=1-49625 cos2(u)=625−49625=576625cos2(u)=625-49625=576625 cos(u)=576625−−−−√cos(u)=576625…
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cot(v−u)cot(v-u) Find the exact value of the trigonometric expression given that sin(u) = -7/25…
sin(u)=−725sin(u)=-725 using pythegorean identity, sin2(u)+cos2(u)=1sin2(u)+cos2(u)=1 (−725)2+cos2(u)=1(-725)2+cos2(u)=1 cos2(u)=1−49625=625−49625=576625cos2(u)=1-49625=625-49625=576625 cos(u)=576625−−−−√=±2425cos(u)=576625=±2425 Since u is in quadrant III ,…
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tan(u−v)tan(u-v) Find the exact value of the trigonometric expression given that sin(u) = -7/25…
Given sin(u)=−725,cos(v)=−45sin(u)=-725,cos(v)=-45 using pythagorean identity, sin2(u)+cos2(u)=1sin2(u)+cos2(u)=1 (−725)2+cos2(u)=1(-725)2+cos2(u)=1 cos2(u)=1−49625=625−49625=576625cos2(u)=1-49625=625-49625=576625 cos(u)=576625−−−−√cos(u)=576625 cos(u)=±2425cos(u)=±2425 since u…
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sin(u+v)sin(u+v) Find the exact value of the trigonometric expression given that sin(u) = -7/25…
Given sin(u)=−725,cos(v)=−45sin(u)=-725,cos(v)=-45 using pythagorean identity, sin2(u)+cos2(u)=1sin2(u)+cos2(u)=1 plug in the value of sin(u), (−725)2+cos2(u)=1(-725)2+cos2(u)=1 49625+cos2(u)=149625+cos2(u)=1 cos2(u)=1−49625cos2(u)=1-49625…
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cos(u+v)cos(u+v) Find the exact value of the trigonometric expression given that sin(u) = -7/25…
Given sin(u)=−725,cos(v)=−45sin(u)=-725,cos(v)=-45 Angles u and v are in quadrant 3. A right triangle can be drawn in quadrant 3. Since sin(u)=−725sin(u)=-725 we know that the side opposite angle u is 7 and the hypotenuse…
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cot(u+v)cot(u+v) Find the exact value of the trigonometric expression given that sin(u) = 5/13…
Given sin(u)=513,cos(v)=−35sin(u)=513,cos(v)=-35 using pythagorean identity, sin2(u)+cos2(u)=1sin2(u)+cos2(u)=1 (513)2+cos2(u)=1(513)2+cos2(u)=1 cos2(u)=1−25169=169−25169=144169cos2(u)=1-25169=169-25169=144169 cos(u)=144169−−−−√cos(u)=144169 cos(u)=±1213cos(u)=±1213 since u is…
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sec(v−u)sec(v-u) Find the exact value of the trigonometric expression given that sin(u) = 5/13…
There are a lot of ways to solve this problem. For instance, one can use the secant sum/difference identity. This identity, however, has a lot of terms. A more elegant solution would be to use the…
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- MATH
csc(u−v)csc(u-v) Find the exact value of the trigonometric expression given that sin(u) = 5/13…
Given sin(u)=513,cos(v)=−35sin(u)=513,cos(v)=-35 using pythagorean identity, sin2(u)+cos2(u)=1sin2(u)+cos2(u)=1 (513)2+cos2(u)=1(513)2+cos2(u)=1 cos2(u)=1−25169=169−25169=144169cos2(u)=1-25169=169-25169=144169 cos(u)=144169−−−−√cos(u)=144169 cos(u)=±1213cos(u)=±1213 since u is…
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tan(u+v)tan(u+v) Find the exact value of the trigonometric expression given that sin(u) = 5/13…
Given sin(u)=513,cos(v)=−35sin(u)=513,cos(v)=-35 Angles u and v are in quadrant 2. A right triangle can be drawn in quadrant 2. Since sin(u)=513sin(u)=513 we know that the side opposite angle u is 5 and the hypotenuse…
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cos(u−v)cos(u-v) Find the exact value of the trigonometric expression given that sin(u) = 5/13…
Given sin(u)=513,cos(v)=−35sin(u)=513,cos(v)=-35 Angles u and v are in quadrant 2. A right triangle can be drawn in quadrant 2. Since sin(u)=513sin(u)=513 you know that the side opposite of angle u is 5 and the hypotenuse…
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- MATH
We know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v).sin(u+v)=sin(u)cos(v)+cos(u)sin(v). sin(u)sin(u)and cos(v)cos(v) are given, let’s find cos(u)cos(u) and sin(v).sin(v). cos(u)=±1−sin2(u)−−−−−−−−−√=±1−25169−−−−−−−√=±144169−−−−√=±1213.cos(u)=±1-sin2(u)=±1-25169=±144169=±1213.Select…
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- MATH
You need to recognize the formula tan(a+b)=tana+tanb1−tana⋅tanb.tan(a+b)=tana+tanb1-tana⋅tanb.You need to put a=25oa=25o and b=110ob=110o , such that:
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- MATH
tan(5π6)−tan(π6)1+tan(5π6)tan(π6)tan(5π6)-tan(π6)1+tan(5π6)tan(π6) Find the exact value of the…
You need to recognize the formulatan(a−b)=tana−tanb1+tana⋅tanbtan(a-b)=tana-tanb1+tana⋅tanb . You need to put a=5π6a=5π6 and b=π6b=π6 , such that:
1 educator answer
- MATH
You need to recognize the formula cos(a−b)=cosa⋅cosb+sina⋅sinbcos(a-b)=cosa⋅cosb+sina⋅sinb . You need to puta=120oa=120oandb=30ob=30o , such that: cos120o⋅cos30o+sin120osin30o=cos(120o−30o)cos120o⋅cos30o+sin120osin30o=cos(120o-30o)
1 educator answer
- MATH
You need to recognize the formula sin(a−b)=sina⋅cosb−cosa⋅sinbsin(a-b)=sina⋅cosb-cosa⋅sinb . You need to put a=120oa=120oand b=60ob=60o , such that: sin120o⋅cos60o−cos120o⋅sin60o=sin(120o−60o)sin120o⋅cos60o-cos120o⋅sin60o=sin(120o-60o)
1 educator answer
- MATH
You need to evaluate the expression using the formula cosa⋅cosb−sina⋅sinb=cos(a+b)cosa⋅cosb-sina⋅sinb=cos(a+b) . You need to put a=π16a=π16and b=3π16,b=3π16, such that:
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- MATH
You need to recognize the formula sin(a+b) = sin a*cos b + sin b*cos a. You need to put a=π12a=π12 and b=π4b=π4 , such that:
1 educator answer
- MATH
You need to recognize the formula tan(a+b)=tana+tanb1−tana⋅tanb.tan(a+b)=tana+tanb1-tana⋅tanb.You need to put a = 2x and b = x , such that: tan(2x+x)=tan2x+tan6x1−tan2x⋅tanxtan(2x+x)=tan2x+tan6x1-tan2x⋅tanx
1 educator answer
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You need to recognize the formula cos(a−b)=cosa⋅cosb+sina⋅sinbcos(a-b)=cosa⋅cosb+sina⋅sinb . You need to put a=3xa=3xand b=2yb=2y , such that: cos3x⋅cos2y+sin3x⋅sin2y=cos(3x−2y)cos3x⋅cos2y+sin3x⋅sin2y=cos(3x-2y) Hence, the given…
1 educator answer
- MATH
You need to recognize the formula tan(a−b)=tana−tanb1+tana⋅tanb.tan(a-b)=tana-tanb1+tana⋅tanb.You need to put a=140oa=140o and b=60ob=60o , such that:
1 educator answer
- MATH
You need to recognize the formula tan(a−b)=tana−tanb1+tana⋅tanb.tan(a-b)=tana-tanb1+tana⋅tanb.You need to put a=45oa=45o and b=30ob=30o , such that:
1 educator answer
- MATH
You need to recognize the formula cos(a+b)=cosa⋅cosb−sina⋅sinb.cos(a+b)=cosa⋅cosb-sina⋅sinb. You need to put a = 130o130oand b = 40o40o , such that: cos130o⋅cos40o−sin130osin40o=cos(130⊕40o)cos130o⋅cos40o-sin130osin40o=cos(130⊕40o)
1 educator answer
- MATH
You need to recognize the formula sin(a+b)=sina⋅cosb+sinb⋅cosasin(a+b)=sina⋅cosb+sinb⋅cosa . You need to put a=60oa=60oand b=15ob=15o , such that: sin(60o+15o)=sin60o⋅cos15o+sin15o⋅cos60osin(60o+15o)=sin60o⋅cos15o+sin15o⋅cos60o
1 educator answer
- MATH
You need to evaluate the expression using the formula cosa⋅cosb−sina⋅sinb=cos(a+b)cosa⋅cosb-sina⋅sinb=cos(a+b) . You need to put a=π7a=π7and b=π5,b=π5, such that:
1 educator answer
- MATH
You need to evaluate the expression using the formula sina⋅cosb−sinb⋅cosa=sin(a−b)sina⋅cosb-sinb⋅cosa=sin(a-b) . You need to put a=3a=3and b=1.2b=1.2 , such that: sin3⋅cos1.2−sin1.2⋅cos3=sin(3−1.2)sin3⋅cos1.2-sin1.2⋅cos3=sin(3-1.2)…
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- MATH
15∘15∘ Find the exact values of the sine, cosine, and tangent of the angle.
You need to find the values of the sine, cosine and tangent of 15o,15o,such that: sin15o=sin(30o2)=1−cos30o2−−−−−−−−−−√sin15o=sin(30o2)=1-cos30o2 sin15o=2−3–√4−−−−−−−√sin15o=2-34
2 educator answers
- MATH
−165∘-165∘ Find the exact values of the sine, cosine, and tangent of the angle.
−165∘=−(120∘+45∘)-165∘=-(120∘+45∘) sin(−165)=−sin(165)sin(-165)=-sin(165) sin(u+v)=sin(u)cos(v)+cos(u)sin(v)sin(u+v)=sin(u)cos(v)+cos(u)sin(v) [sin(−(u+v))]=−[sin(u)cos(v)+cos(u)sin(v)][sin(-(u+v))]=-[sin(u)cos(v)+cos(u)sin(v)] [sin(−(120+45))]=−[sin(120)cos(45)+cos(120)sin(45)][sin(-(120+45))]=-[sin(120)cos(45)+cos(120)sin(45)]…
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- MATH
−105∘-105∘ Find the exact values of the sine, cosine, and tangent of the angle.
−105∘=30∘−135-105∘=30∘-135 sin(u−v)=sin(u)cos(v)−cos(u)sin(v)sin(u-v)=sin(u)cos(v)-cos(u)sin(v) sin(30−135)=sin(30)cos(135)−cos(30)sin(135)sin(30-135)=sin(30)cos(135)-cos(30)sin(135) sin(30−135)=(12)(−2–√2)−(3–√2)(2–√2)=−2–√4(1+3–√)sin(30-135)=(12)(-22)-(32)(22)=-24(1+3)…
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- MATH
285∘285∘ Find the exact values of the sine, cosine, and tangent of the angle.
285∘=225∘+60∘285∘=225∘+60∘ sin(u+v)=sin(u)cos(v)+cos(u)sin(v)sin(u+v)=sin(u)cos(v)+cos(u)sin(v) sin(225+60)=sin(225)cos(60)+cos(225)sin(60)sin(225+60)=sin(225)cos(60)+cos(225)sin(60) sin(225+60)=(−2–√2)(12)+(−2–√2)(3–√2)=−2–√4(1+3–√)sin(225+60)=(-22)(12)+(-22)(32)=-24(1+3)…
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- MATH
5π125π12 Find the exact values of the sine, cosine, and tangent of the angle.
5π12=π4+π65π12=π4+π6 sin(u+v)=sin(u)cos(v)+cos(u)sin(v)sin(u+v)=sin(u)cos(v)+cos(u)sin(v) sin(π4+π6)=sin(π4)cos(π6)+cos(π4)sin(π6)sin(π4+π6)=sin(π4)cos(π6)+cos(π4)sin(π6) sin(π4+π6)=(2–√2)(3–√2)+(2–√2)(12)=2–√4(3–√+1)sin(π4+π6)=(22)(32)+(22)(12)=24(3+1)…
1 educator answer
- MATH
−13π12-13π12 Find the exact values of the sine, cosine, and tangent of the angle.
sin(−13π12)sin(-13π12) using the property sin(-x)=-sin(x), sin(−13π12)=−sin(13π12)sin(-13π12)=-sin(13π12) =−sin(π2+π3+π4)=-sin(π2+π3+π4) Now using sin(pi/2+x)=cos(x), =−cos(π3+π4)=-cos(π3+π4)…
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- MATH
−7π12-7π12 Find the exact values of the sine, cosine, and tangent of the angle.
sin(−7π12)=−sin(7π12)sin(-7π12)=-sin(7π12) =−sin(π3+π4)=-sin(π3+π4) using the identity sin(x+y)=sin(x)cos(y)+cos(x)sin(y)sin(x+y)=sin(x)cos(y)+cos(x)sin(y) =−(sin(π3)cos(π4)+cos(π3)sin(π4))=-(sin(π3)cos(π4)+cos(π3)sin(π4)) =−(3–√2⋅12–√+12⋅12–√)=-(32⋅12+12⋅12)…
1 educator answer
- MATH
13π1213π12 Find the exact values of the sine, cosine, and tangent of the angle.
sin(13π12)=sin(π2+π3+π4)sin(13π12)=sin(π2+π3+π4) As we know that sin(π2+θ)=cos(θ)sin(π2+θ)=cos(θ) ∴sin(13π12)=cos(π3+π4)∴sin(13π12)=cos(π3+π4) Now use the identity cos(x+y)=cos(x)cos(y)−sin(x)sin(y)cos(x+y)=cos(x)cos(y)-sin(x)sin(y)…
2 educator answers
- MATH
225∘=300∘−45∘225∘=300∘-45∘ Find the exact values of the sine, cosine, and tangent of the angle.
sin(u−v)=sin(u)cos(v)−cos(u)sin(v)sin(u-v)=sin(u)cos(v)-cos(u)sin(v) sin(300−45)=sin(300)cos(45)−cos(300)sin(45)sin(300-45)=sin(300)cos(45)-cos(300)sin(45) sin(300−45)=(−3–√2)(2–√2)−(12)(2–√2)=−2–√4(3–√+1)sin(300-45)=(-32)(22)-(12)(22)=-24(3+1)cos(u−v)=cos(u)cos(v)+sin(u)sin(v)cos(u-v)=cos(u)cos(v)+sin(u)sin(v)…
1 educator answer
- MATH
195∘=225∘−30∘195∘=225∘-30∘ Find the exact values of the sine, cosine, and tangent of the angle.
sin(u−v)=sin(u)cos(v)−cos(u)sin(v)sin(u-v)=sin(u)cos(v)-cos(u)sin(v) sin(225−30)=sin(225)cos(30)−cos(225)sin(30)sin(225-30)=sin(225)cos(30)-cos(225)sin(30) sin(225−30)=(−2–√2)(3–√2)−(−2–√2)(12)=−2–√4(3–√−1)sin(225-30)=(-22)(32)-(-22)(12)=-24(3-1)cos(u−v)=cos(u)cos(v)+sin(u)sin(v)cos(u-v)=cos(u)cos(v)+sin(u)sin(v)…
1 educator answer
- MATH
165∘=135∘+30∘165∘=135∘+30∘ Find the exact values of the sine, cosine, and tangent of the angle.
sin(u+v)=sin(u)cos(v)+cos(u)sin(v)sin(u+v)=sin(u)cos(v)+cos(u)sin(v) sin(135+30)=sin(135)cos(30)+cos(135)sin(30)sin(135+30)=sin(135)cos(30)+cos(135)sin(30) sin(135+30)=(2–√2)(3–√2)+(−2–√2)(12)sin(135+30)=(22)(32)+(-22)(12) sin(135+30)=6–√4−2–√4=2–√4(3–√−1)sin(135+30)=64-24=24(3-1)…
1 educator answer
- MATH
105∘=60∘+45∘105∘=60∘+45∘ Find the exact values of the sine, cosine, and tangent of the angle.
You need to evaluate the sine of 105o105o , using the formula sin(a+b)=sina⋅cosb+sinb⋅cosasin(a+b)=sina⋅cosb+sinb⋅cosa such that: sin(105o)=sin(60o+45o)=sin60o⋅cos45o+sin45o⋅cos60osin(105o)=sin(60o+45o)=sin60o⋅cos45o+sin45o⋅cos60o
1 educator answer
- MATH
−π12=π6−π4-π12=π6-π4 Find the exact values of the sine, cosine, and tangent of the angle.
You need to find the values of sine and cosine of −π12-π12 , using the formulas sin(a−b)=sina⋅cosb−sinb⋅cosasin(a-b)=sina⋅cosb-sinb⋅cosa and cos(a−b)=cosa⋅cosb+sina⋅sinbcos(a-b)=cosa⋅cosb+sina⋅sinb , such that:
1 educator answer
- MATH
17π12=9π4−5π617π12=9π4-5π6 Find the exact values of the sine, cosine, and tangent of…
sin(u−v)=sin(u)cos(v)−cos(u)sin(v)sin(u-v)=sin(u)cos(v)-cos(u)sin(v) sin(9π4−5π6)=sin(9π4)cos(5π6)−cos(9π4)sin(5π6)sin(9π4-5π6)=sin(9π4)cos(5π6)-cos(9π4)sin(5π6) sin(9π4−5π6)=(2–√2)(−3–√2)−(2–√2)(12)=−2–√4(3–√+1)sin(9π4-5π6)=(22)(-32)-(22)(12)=-24(3+1)…
1 educator answer
- MATH
7π12=π3+π47π12=π3+π4 Find the exact values of the sine, cosine, and tangent of the angle.
You need to evaluate the sine of 7π127π12 , using the formula sin(a+b)=sina⋅cosb+sinb⋅cosasin(a+b)=sina⋅cosb+sinb⋅cosa such that: sin(7π12)=sin(π3+π4)=sin(π3)⋅cos(π4)+sin(π4)⋅cos(π3)sin(7π12)=sin(π3+π4)=sin(π3)⋅cos(π4)+sin(π4)⋅cos(π3)…
1 educator answer
- MATH
11π12=3π4+π611π12=3π4+π6 Find the exact values of the sine, cosine, and tangent of the…
sin(u+v)=sin(u)cos(v)+cos(u)sin(v)sin(u+v)=sin(u)cos(v)+cos(u)sin(v) sin(3π4+π6)=sin(3π4)cos(π6)+cos(3π4)sin(π6)sin(3π4+π6)=sin(3π4)cos(π6)+cos(3π4)sin(π6) sin(3π4+π6)=(2–√2)(3–√2)+(−2–√2)(12)=(2–√4)(3–√−1)sin(3π4+π6)=(22)(32)+(-22)(12)=(24)(3-1)…
1 educator answer
- MATH
cos(120+45),cos(120)+cos(45)cos(120+45),cos(120)+cos(45) Find the exact value of the expression.
Given cos(120+45)cos(120+45) cos(u+v)=cos(u)cos(v)−sin(u)sin(v)cos(u+v)=cos(u)cos(v)-sin(u)sin(v) cos(120+45)=cos(120)cos(45)−sin(120)sin(45)cos(120+45)=cos(120)cos(45)-sin(120)sin(45) cos(120+45)=(−12)(2–√2)−(3–√2)(2–√2)=−2–√4−6–√4=−2–√−6–√4cos(120+45)=(-12)(22)-(32)(22)=-24-64=-2-64Given…
1 educator answer
- MATH
sin(135−30),sin(135)−sin(30)sin(135-30),sin(135)-sin(30) Find the exact value of the expression.
sin(1350−300)=sin1350⋅cos300−cos1350⋅sin300sin(1350-300)=sin1350⋅cos300-cos1350⋅sin300 (we know that =sin(90+45)⋅cos30−cos(90+45)⋅sin300=sin(90+45)⋅cos30-cos(90+45)⋅sin300
1 educator answer
- MATH
sin(7π6−π3),sin(7π6)−sin(π3)sin(7π6-π3),sin(7π6)-sin(π3) Find the exact value of the expression.
sin(u−v)=sin(u)cos(v)−cos(u)sin(v)sin(u-v)=sin(u)cos(v)-cos(u)sin(v) sin(7π6−π3)=sin(7π6)cos(π3)−cos(7π6)sin(π3)sin(7π6-π3)=sin(7π6)cos(π3)-cos(7π6)sin(π3) sin(7π6−π3)=(−12)(12)−(−3–√2)(3–√2)sin(7π6-π3)=(-12)(12)-(-32)(32) sin(7π6−π3)=−14+34=24=12sin(7π6-π3)=-14+34=24=12…
1 educator answer
- MATH
cos(π4+π3),cos(π4)+cos(π3)cos(π4+π3),cos(π4)+cos(π3) Find the exact value of each expression.
cos(u+v)=cos(u)cos(v)−sin(u)sin(v)cos(u+v)=cos(u)cos(v)-sin(u)sin(v) cos(π4+π3)=cos(π4)cos(π3)−sin(π4)sin(π3)cos(π4+π3)=cos(π4)cos(π3)-sin(π4)sin(π3) cos(π4+π3)=(2–√2)(12)−(2–√2)(3–√2)=2–√4−6–√4=(2–√4)(1−3–√)cos(π4+π3)=(22)(12)-(22)(32)=24-64=(24)(1-3)…
1 educator answer
- MATH
y=x3−x+1,y=−x4+4x−1y=x3-x+1,y=-x4+4x-1 Use a graph to estimate the x-coordinates of the points…
y=x3−x+1y=x3-x+1 y=−x4+4x−1y=-x4+4x-1 The graph of the two equations are: (Green curve graph of y=x3−x+1y=x3-x+1 . Blue curve graph of y=−x4+4x−1y=-x4+4x-1 .) Base on the graph, the curve curves intersect at…
1 educator answer
- MATH
y=ex,y=x−−√+1y=ex,y=x+1 Use a graph to estimate the x-coordinates of the points of…
y=exy=ex y=x−−√+1y=x+1 The graph of these two equations are: (Green curve graph of y=exy=ex . And blue curve is the graph of y=x−−√+1y=x+1 .) Base on the graph, the two curve intersect at x=0x=0…
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- MATH
This is the solid obtained by rotating the region under the curve y=cos(x)−sin(x)y=cos(x)-sin(x) , above y=0 from x=0 to x=π4π4 , about the line x=ππ .
1 educator answer