Question 1

Which of the following best describes the definition of circular functions for any real number $$s$$?

Accepted Answer

They are defined using the unit circle, where $$s is $$the length of an arc measured from $$(1,0).$$

Question 2

Given the point $$(x, y) on $$the unit circle corresponding to an arc length $$s$$, which formula correctly gives $$	an s$$?

Accepted Answer

$$	an s = \dfrac{y}{x}$$

Question 3

Evaluate $$\sin\left(\dfrac{3\pi}{2}\right)$$ using the unit circle.

Accepted Answer

$$-1$$

Question 4

Which of the following is undefined for $$s = \dfrac{3\pi}{2}$$?

Accepted Answer

$$	an s$$

Question 5

If $$s = \dfrac{7\pi}{4}$$, what is $$	an s$$?

Accepted Answer

$$-1$$

Question 6

Given $$s = \dfrac{5\pi}{6}$$, what is $$\cos s$$?

Accepted Answer

$$-\dfrac{\sqrt{3}}{2}$$

Question 7

Which calculator setting is required to correctly evaluate circular functions of real numbers?

Accepted Answer

Radian mode

Question 8

If $$\cos s = 0.457$$ and $$s \in [0, \pi/2]$$, what is the value of $$s to $$three decimal places?

Accepted Answer

$$1.096$$

Question 9

The phase $$F(t) of $$the moon is given by $$F(t) = \dfrac{1}{2}(1 - \cos t). $$What is $$F(\pi)$$ and what does it represent?

Accepted Answer

$$F(\pi) = 1$$, full moon

Question 10

A tide at Clearwater Beach is modeled by $$f(x) = 0.6 \cos[0.511(x - 2.4)] + 2. $$What is the estimated tide level when $$x = 10$$?

Accepted Answer

$$1.56$$ feet

Question 11

Which of the following is the correct definition for $$\sec s on $$the unit circle?

Accepted Answer

$$\sec s = \dfrac{1}{x}$$

Question 12

If $$	heta = 30^\circ$$, what is $$\sin 	heta in $$terms of segment length in a right triangle?

Accepted Answer

$$\sin 	heta = \dfrac{1}{2}$$

Question 13

Which of the following is true about the coterminal angle of $$-\dfrac{5\pi}{3}$$?

Accepted Answer

It is coterminal with $$\dfrac{\pi}{3}.$$

Question 14

What is the difference in water level between high tide and low tide if high tide is $$2.6$$ feet and low tide is $$1.4$$ feet?

Accepted Answer

$$1.2$$ feet

Question 15

If $$	heta = 30^\circ$$, what is $$\cot 	heta$$?

Accepted Answer

$$\cot 	heta = \sqrt{3}$$

Question 16

Which of the following is the correct value for $$	an\left(\dfrac{\pi}{3}ight)$$?

Accepted Answer

$$\sqrt{3}$$

Question 17

If $$	heta = 30^\circ$$, what is $$\sec 	heta$$?

Accepted Answer

$$\dfrac{2}{\sqrt{3}}$$

Question 18

Which of the following is the correct value for $$\sin\left(\dfrac{5\pi}{6}\right)$$?

Accepted Answer

$$\dfrac{1}{2}$$

Question 19

Which of the following is the correct value for $$	an\left(-\dfrac{5\pi}{3}ight)$$?

Accepted Answer

$$\sqrt{3}$$

Chapter 9.5: Circular Functions – Definitions, Evaluation, and Applications

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