Question 1

Given the point $$\left( \frac{5}{13}, \frac{12}{13} ight) on $$the unit circle as the terminal side of angle $$	heta in $$standard position, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{12}{13}$$

Question 2

For the same angle $$	heta as in $$the previous question, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{5}{13}$$

Question 3

Given $$\sin 	heta = \frac{12}{13}$$ and $$\cos 	heta = \frac{5}{13}$$, what is $$	an 	heta$$?

Accepted Answer

$$\frac{12}{5}$$

Question 4

If $$\sin 	heta = \frac{12}{13}$$ and $$\cos 	heta = \frac{5}{13}$$, what is $$\csc 	heta$$?

Accepted Answer

$$\frac{13}{12}$$

Question 5

Given $$\cos 	heta = \frac{5}{13}$$, what is $$\sec 	heta$$?

Accepted Answer

$$\frac{13}{5}$$

Question 6

Given $$	an 	heta = \frac{12}{5}$$, what is $$\cot 	heta$$?

Accepted Answer

$$\frac{5}{12}$$

Question 7

A ladder leans against a wall, forming an angle $$	heta$$ with the ground. If the top of the ladder touches the wall at a height of 12 ft and the base is 5 ft from the wall, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{12}{13}$$

Question 8

If $$\sin 	heta = \frac{12}{13}$$ and $$	heta is in $$the first quadrant, what is $$\cos(90^\circ - 	heta)$$?

Accepted Answer

$$\frac{12}{13}$$

Question 9

A point $$P on $$the unit circle has coordinates $$\left( \frac{5}{13}, \frac{12}{13} \right). $$What is the equation relating $$x$$ and $$y$$ for any point on the unit circle?

Accepted Answer

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

Question 10

If $$\sin 	heta = \frac{12}{13}$$ and $$\cos 	heta = \frac{5}{13}$$, which of the following is the value of $$\sin^2$ 	heta + \cos^2$ 	heta$$?

Accepted Answer

$$1$$

Question 11

A wheel of radius 1 unit rolls along the x-axis. If a point on the rim starts at $$(1,0)$$, what are the coordinates after a rotation of $$	heta$$ radians?

Accepted Answer

$$(\cos 	heta, \sin 	heta)$$

Question 12

If $$\sin 	heta = \frac{12}{13}$$ and $$	heta is in $$the first quadrant, what is the value of $$\sin(-	heta)$$?

Accepted Answer

$$-\frac{12}{13}$$

Question 13

A ramp rises 12 meters over a horizontal distance of 5 meters. What is the angle $$	heta$$ the ramp makes with the ground, in terms of $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{12}{5}$$

Question 14

If $$\sin 	heta = \frac{12}{13}$$ and $$\cos 	heta = \frac{5}{13}$$, what is $$\sin(2	heta)$$?

Accepted Answer

$$\frac{120}{169}$$

Question 15

If $$\sin 	heta = \frac{12}{13}$$ and $$\cos 	heta = \frac{5}{13}$$, what is $$\cos(2	heta)$$?

Accepted Answer

$$-\frac{119}{169}$$

Evaluating Circular Function Values Using the Unit Circle

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