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

**MATH**

**arcsin(−0.125)arcsin(-0.125) Use a calculator to evaluate the expression. Round your result to two…**

Plug in the expression into the calculator. −0.13-0.13

**MATH**

**arccos(−0.41)arccos(-0.41) Use a calculator to evaluate the expression. Round your result to two…**

Plug in the expression into the calculator. 1.991.99

**MATH**

**cos−1(0.26)cos-1(0.26) Use a calculator to evaluate the expression. Round your result to two…**

Plug in the expression into the calculator. 1.311.31

**MATH**

**sin−1(0.31)sin-1(0.31) Use a calculator to evaluate the expression. Round your result to two…**

Plug in the expression into the calculator. 0.320.32

**MATH**

**arctan(25)arctan(25) Use a calculator to evaluate the expression. Round your result to two decimal…**

Plug in the expression into the calculator. 1.531.53

**MATH**

**arctan(−3)arctan(-3) Use a calculator to evaluate the expression. Round your result to two decimal…**

Plug in the expression into the calculator. −1.25-1.25

**MATH**

Plug in the expression into the calculator. 2.352.35

**MATH**

**arcsin(−0.75)arcsin(-0.75) Use a calculator to evaluate the expression. Round your result to two…**

Plug in the expression into the calculator. −0.85-0.85

**MATH**

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**

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

**MATH**

**y=(13)sec(πx2+(π2))y=(13)sec(πx2+(π2)) Use a graphing utility to graph the function. (Include two…**

Make a graph of the function (refer to the attached image)

**MATH**

**y=0.1tan(πx4+(π4))y=0.1tan(πx4+(π4)) Use a graphing utility to graph the function. (Include two…**

Graph the function (refer to the attached image)

**MATH**

**y=2sec(2x−π)y=2sec(2x-π) Use a graphing utility to graph the function. (Include two full periods.)**

Graph

**MATH**

**y=−csc(4x−π)y=-csc(4x-π) Use a graphing utility to graph the function. (Include two full periods.)**

Graph

**MATH**

**y=(14)cot(x−(π2))y=(14)cot(x-(π2)) Use a graphing utility to graph the function. (Include two full…**

Graph

**MATH**

**y=tan(x−(π4))y=tan(x-(π4)) Use a graphing utility to graph the function. (Include two full periods.)**

Graph

**MATH**

**y=sec(πx)y=sec(πx) Use a graphing utility to graph the function. (Include two full periods.)**

Make a graph of the function (refer to the attached image)

**MATH**

**y=−2sec(4x)y=-2sec(4x) Use a graphing utility to graph the function. (Include two full periods.)**

Graph

**MATH**

**y=−tan(2x)y=-tan(2x) Use a graphing utility to graph the function. (Include two full periods.)**

Graph

**MATH**

**y=tan(x3)y=tan(x3) Use a graphing utility to graph the function. (Include two full periods.)**

Graph

**MATH**

**y=2cot(x+(π2))y=2cot(x+(π2)) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=(14)csc(x+(π4))y=(14)csc(x+(π4)) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=−sec(πx)+1y=-sec(πx)+1 Sketch the graph of the function. (Include two full periods.)**

Make a graph of the function (refer to the attached image)

**MATH**

**y=2sec(x+π)y=2sec(x+π) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=csc(2x−π)y=csc(2x-π) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=2csc(x−π)y=2csc(x-π) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=tan(x+π)y=tan(x+π) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=tan(πx4)y=tan(πx4) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=(−12)tan(x)y=(-12)tan(x) Sketch the graph of the function. (Include two full periods.)**

Graph

**MATH**

**y=2sec(3x)y=2sec(3x) Sketch the graph of the function. (Include two full periods.)**

Graph