Reference angles and angles in the unit circle Quiz 1

Question 1

Find the reference angle of $$\dfrac{11\pi }{5}$$

Accepted Answer

$$\dfrac{\pi }{5}$$

Answer

$$\dfrac{11\pi }{5}$$

Answer

$$2\pi $$

Answer

none of these

Question 2

Find the angle in the third quadrant that has a reference angle $$\dfrac{2\pi }{7}$$.

Accepted Answer

$$\dfrac{9\pi }{7}$$

Answer

$$\dfrac{5\pi }{7}$$

Answer

$$\dfrac{12\pi }{7}$$

Answer

$$\dfrac{14\pi }{7}$$

Question 3

Find the coordinates of the point on the unit circle at an angle of $$\dfrac{7\pi }{6}$$

Accepted Answer

$$\left( -\dfrac{\sqrt{3}}{2},-\dfrac{1}{2} \right)$$

Answer

$$\left( \dfrac{\sqrt{3}}{2},\dfrac{1}{2} \right)$$

Answer

$$\left( -\dfrac{\sqrt{3}}{2},\dfrac{1}{2} \right)$$

Answer

$$\left( \dfrac{\sqrt{3}}{2},-\dfrac{1}{2} \right)$$

Question 4

Using a reference angle. Find the exact value of $${{\cos }^{2}}\left( {{150}^{\circ }} \right)-{{\sin }^{2}}\left( {{150}^{\circ }} \right)$$

Accepted Answer

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

Answer

$$\dfrac{1}{4}$$

Answer

$$-\dfrac{1}{4}$$

Answer

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

Question 5

A certain angle $$	heta $$ corresponds to a point on the unit circle at $$\left( -\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2} ight)$$. Find the value of $$	an 	heta $$.

Accepted Answer

-1

Answer

1

Answer

0

Answer

infinity