Loading [MathJax]/jax/output/HTML-CSS/jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

3.4.1: Exercises 3.4

( \newcommand{\kernel}{\mathrm{null}\,}\)

Terms and Concepts

Exercise 3.4.1.1

Explain why the domain of tangent is restricted.

Answer

Tangent is undefined whenever cosine is 0.

Exercise 3.4.1.2

Explain why the domain of cosecant is restricted.

Answer

Cosecant is undefined whenever sine is 0.

Exercise 3.4.1.3

Explain what is meant by the range of a function.

Answer

The range describes the possible output values of the function.

Exercise 3.4.1.4

What do the coordinates on the unit circle tell you?

Answer

The x coordinate tells you the value of cosine for that angle and the y coordinate tells you the value of sine for that angle.

Exercise 3.4.1.5

Sketch the unit circle from memory. Use Figure 3.4.2 to check your work and add in any values you could not remember.

Answer

Problems

Evaluate each statement given in exercises 3.4.1.6 - 3.4.1.10.

Exercise 3.4.1.6

tan(π4)

Answer

1

Exercise 3.4.1.7

cos(π4)

Answer

22

Exercise 3.4.1.8

sin(3π4)

Answer

22

Exercise 3.4.1.9

csc(3π4)

Answer

2

Exercise 3.4.1.10

sin(3π2)

Answer

1

Determine the range of each function given in exercises 3.4.1.11 - 3.4.1.14.

Exercise 3.4.1.11

f(x)=2sin(4x)+3

Answer

[1,5]

Exercise 3.4.1.12

g(x)=6cos(2x)8

Answer

[14,2]

Exercise 3.4.1.13

h(x)=sin(x)1

Answer

[2,0]

Exercise 3.4.1.14

f(θ)=4sin(θπ)

Answer

[4,4]

In exercises 3.4.1.15 - 3.4.1.18, use the unit circle to help you answer the given question.

Exercise 3.4.1.15

Find the ordered pair for the point on the unit circle associated with θ=5π4

Answer

(22,22)

Exercise 3.4.1.16

Sketch the a unit circle and the angle represented by θ=7π6. Find the ordered pair where this line intersects the unit circle and label this point on your sketch.

Answer

Exercise 3.4.1.17

Sketch the a unit circle and the angle represented by θ=2π3. Find the ordered pair where this line intersects the unit circle and label this point on your sketch.

Answer

Exercise 3.4.1.18

Find the equation of the line that intersects the unit circle at θ=π and at θ=π3. Answer in slope intercept form.

Answer

y=33x+33


3.4.1: Exercises 3.4 is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

Support Center

How can we help?