Q: Which of the following statements is true about the cosine function on the unit circle?

$$\cos(\theta) is an $$even function$

Question 1

Which of the following equations represents the unit circle centered at the origin?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 2

If a point $$(x, y)$$ lies on the unit circle and $$x = \frac{1}{2}$$, what is a possible value for $$y$$?

Accepted Answer

$$y = \frac{\sqrt{3}}{2}$$

Question 3

What are the coordinates on the unit circle corresponding to $$	heta = \frac{\pi}{2}$$?

Accepted Answer

$$(0, 1)$$

Question 4

Which trigonometric function is defined as the $$y-$$coordinate of a point on the unit circle?

Accepted Answer

$$\sin(	heta)$$

Question 5

Given a $$30^\circ$$-$$60^\circ$$-$$90^\circ$$ triangle with hypotenuse $$2$$, what is the length of the side opposite the $$30^\circ$$ angle?

Accepted Answer

$$1$$

Question 6

Evaluate $$\sin\left(\frac{\pi}{4}\right)$$ using special triangles.

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 7

Which of the following is the exact value of $$\cos\left(\frac{2\pi}{3}\right)$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 8

Find the exact value of $$	an\left(\frac{11\pi}{6}ight).$$

Accepted Answer

$$-\frac{1}{\sqrt{3}}$$

Question 9

Which of the following statements is true about the cosine function on the unit circle?

Accepted Answer

$$\cos(	heta) is an $$even function$

Question 10

If $$\sin(	heta) = \frac{1}{2}$$ and $$	heta is in $$the second quadrant, what is $$	heta$$?

Accepted Answer

$$	heta = \frac{5\pi}{6}$$

Question 11

Which of the following is undefined?

Accepted Answer

$$\sec\left(\frac{\pi}{2}\right)$$

Question 12

A Ferris wheel has a radius of 1 unit and is centered at the origin. If a seat is at the point $$(\frac{\sqrt{3}}{2}, \frac{1}{2})$$, what is the angle (in radians) from the positive $$x-$$axis?

Accepted Answer

$$\frac{\pi}{6}$$

Question 13

Which of the following is the reference angle for $$\frac{7\pi}{6}$$?

Accepted Answer

$$\frac{\pi}{6}$$

Question 14

Evaluate $$\csc\left(\frac{4\pi}{3}\right).$$

Accepted Answer

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

Question 15

Which of the following is the $$x-$$coordinate of the point on the unit circle corresponding to $$	heta = \frac{5\pi}{3}$$?

Accepted Answer

$$\frac{1}{2}$$

Question 16

If $$	an(	heta) = 1$$ and $$	heta is in $$the third quadrant, what is $$	heta$$?

Accepted Answer

$$\frac{5\pi}{4}$$

Question 17

Which of the following is the exact value of $$\cot\left(\frac{7\pi}{4}\right)$$?

Accepted Answer

$$-1$$

Question 18

If $$\sin(	heta) = -1$$, what is $$	heta$$?

Accepted Answer

$$\frac{3\pi}{2}$$

Question 19

Which of the following is the value of $$	an\left(\frac{2\pi}{3}ight)$$?

Accepted Answer

$$-\sqrt{3}$$

Question 20

A rotating platform makes one full revolution every 2 seconds. If a point starts at $$(1, 0)$$, what are its coordinates after $$\frac{1}{2}$$ second?

Accepted Answer

$$(0, 1)$$

The Unit Circle and Special Triangles in Trigonometry

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