y=2csc(x−π)y=2csc(x-π) Sketch the graph of the function

arcsin(.65) is equivalent to 0.707584437 rad and because there is a 7 behind the second decimal place, we round up as 7 is bigger than 5, so we should end up with: .71

MATH

arccos(0.37)arccos(0.37) Use a calculator to evaluate the expression. Round your result to two decimal…

Plug in the expression into your calculator. Remember that arccos is the same as cos−1cos-1 Therefore, after plugging in the expression, you get 1.191.19 radians.

MATH

tan−1(−3–√3)tan-1(-33) Evaluate the expression without using a calculator.

You need to find value for which tan equals −3–√3-33 . Using a unit circle, it can be determined that the answer is −π6-π6

MATH

sin−1(−3–√2)sin-1(-32) Evaluate the expression without using a calculator.

You need to find value for which sin equals −3–√2-32 . Using a unit circle, it can be determined that the answer is −π3-π3

MATH

arcsin(2–√2)arcsin(22) Evaluate the expression without using a calculator.

You need to find value for which sin equals 2–√222 . Using a unit circle, it can be determined that the answer is π4π4

MATH

arccos(−12)arccos(-12) Evaluate the expression without using a calculator.

You need to find value for which cos equals −12-12 . Using a unit circle, it can be determined that the answer is 2π32π3

MATH

arctan(3–√)arctan(3) Evaluate the expression without using a calculator.

You need to find value for which tan equals 3–√3 . Using a unit circle, it can be determined that the answer is π3π3

MATH

arctan(−3–√)arctan(-3) Evaluate the expression without using a calculator.

You need to find value for which tan equals −3–√-3 . Using a unit circle, it can be determined that the answer is −π3-π3

MATH

sin−1(−2–√2)sin-1(-22) Evaluate the expression without using a calculator.

This asks you what value of sin equals −2–√2-22 (sinx=−2–√2sinx=-22 . Remember that sin is y values . Using a unit circle, you can determine that the answer is −π4-π4 .

MATH

cos−1(−3–√2)cos-1(-32) Evaluate the expression without using a calculator.

You need to find value for which cos equals −3–√2-32 . Using a unit circle, it can be determined that the answer is 5π65π6

MATH

arctan(1)arctan(1) Evaluate the expression without using a calculator.

This asks you what value of tan equals 1 (tanx=1tanx=1 ). Remember that tan is y/x. Using a unit circle, you can determine that the answer is π4π4 .

MATH

arctan(3–√3)arctan(33) Evaluate the expression without using a calculator.

This question is asking what value of tan will give me 3–√333 (tanx=3–√3tanx=33 ). Using a unit circle, you can determine that the answer is π6π6 .

MATH

arccos(0)arccos(0) Evaluate the expression without using a calculator.

Essentially, the question is asking what value of cos gives me 0 (cosx=0cosx=0 ). Using a unit circle, you can find the answer to be π2π2 .

MATH

arccos(12)arccos(12) Evaluate the expression without using a calculator.

You need to find what value of cos gives an answer of 1/2 (cosx=12cosx=12). Using a unit circle, one can find the answer to be π3π3 .

MATH

arcsin(0)arcsin(0) Evaluate the expression without using a calculator.

You need to find the value where the sin of some value give me 0 (sinx=0sinx=0 ). Using the unit circle, one can devise that the answer is 00 .

MATH

arcsin(12)arcsin(12) Evaluate the expression without using a calculator.

arcsin(12)arcsin(12) is the value whose sinsin equals 1212 . What angle has a sine equal to 1/2? π6π6

MATH

h(x)=xsin(1x)h(x)=xsin(1x) Use a graphing utility to graph the function. Describe the behavior of…

Graph, It looks like y approaches 0 when x approaches 0, but x=0 is undefined.

MATH

f(x)=sin(1x)f(x)=sin(1x) Use a graphing utility to graph the function. Describe the behavior of the…

Graph: It approaches zero, but it never gets there (limit does not exist).

MATH

y=(6x)+cos(x),x>0y=(6x)+cos(x),x>0 Use a graphing utility to graph the function. Describe the…

Clearly at x=0 the function is not defined.As x−>0,y−>∞x->0,y->∞

MATH

g(x)=cot(x)g(x)=cot(x) Use the graph of the function to determine whether the function is even,…

The graph of g(x)=cot(x) is shown below. We know that sin(-x)=-sin(x) and cos(-x)=cos(x). So, cot(−x)=cos(−x)sin(−x)=cos(x)−sin(x)=−cot(x)cot(-x)=cos(-x)sin(-x)=cos(x)-sin(x)=-cot(x) Hence, cot (x) is an odd function, and…

1 educator answer

MATH

f(x)=tan(x)f(x)=tan(x) Use the graph of the function to determine whether the function is even,…

The graph of the functionis symmetric about origin.So it is an odd function. f(x)=tanx f(-x)=tan(-x) =-tanx =-f(x). f(-x)=-f(x).So the function is odd.

MATH

f(x)=sec(x)f(x)=sec(x) Use the graph of the function to determine whether the function is even,…

It is even. cos−x=cos(0−x)cos-x=cos(0-x) cos(0−x)=sin0sinx+cos0cosx=cosxcos(0-x)=sin0sinx+cos0cosx=cosx Therefore, coscos is even sec(−x)=1cos−xsec(-x)=1cos-x This equals 1cosx=secx1cosx=secx Therefore, secsecis even