$$\frac{2\tan A}{1-\tan^2$ A}$$

Question 1

Given $$\sin(	heta) = \frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos(	heta)$$?

Accepted Answer

$$-\frac{4}{5}$$

Question 2

If $$	an(\alpha) = 2$$ and $$	an(\beta) = 3$$, what is $$	an(\alpha + \beta)$$?

Accepted Answer

$$\frac{2+3}{1-2\cdot3}$$

Question 3

Which of the following is equivalent to $$\cos(2	heta)$$?

Accepted Answer

$$1 - 2\sin^2$	heta$$

Question 4

A ladder leans against a wall forming a $$60^\circ$$ angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach?

Accepted Answer

$$10 \cdot \sin 60^\circ$$

Question 5

Simplify $$	an	heta \cos	heta \csc	heta.$$

Accepted Answer

$$\sin	heta$$

Question 6

Find the exact value of $$\cos(75^\circ)$$ using sum and difference identities.

Accepted Answer

$$\frac{\sqrt{6} - \sqrt{2}}{4}$$

Question 7

If $$\cos	heta = -\frac{1}{2}$$ and $$	heta is in $$Quadrant III, what is $$	heta in $$radians?

Accepted Answer

$$\frac{4\pi}{3}$$

Question 8

Which identity is used to express $$\sin(A+B) in $$terms of $$\sin$$ and $$\cos$$?

Accepted Answer

$$\sin A \cos B + \cos A \sin B$$

Question 9

Find the exact value of $$2\cos^2$ 22.5^\circ - 1.$$

Accepted Answer

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

Question 10

If $$\sin	heta = -\frac{1}{2}$$, what is $$	heta in $$degrees in the range $$[-90^\circ, 90^\circ]$$?

Accepted Answer

$$-30^\circ$$

Question 11

A Ferris wheel has a radius of 20 meters. If a seat is at an angle of $$45^\circ$$ above the horizontal, how high above the center is the seat?

Accepted Answer

$$20 \cdot \sin 45^\circ$$

Question 12

Which of the following is the correct double angle identity for $$	an(2A)$$?

Accepted Answer

$$\frac{2	an A}{1-	an^2$ A}$$

Question 13

If $$\cos(\alpha) = \frac{1}{3}$$ and $$\alpha is in $$Quadrant I, what is $$\sin(2\alpha)$$?

Accepted Answer

Question 14

Which equation correctly expresses $$1 + 	an^2$	heta$$?

Accepted Answer

$$\sec^2$	heta$$

Question 15

Find the exact value of $$\sin(76^\circ)\cos(31^\circ) - \cos(76^\circ)\sin(31^\circ).$$

Accepted Answer

$$\sin(45^\circ)$$

Question 16

If $$\sin(	heta) = \frac{1}{2}$$ and $$	heta is in $$Quadrant II, what is $$	heta in $$degrees?

Accepted Answer

$$150^\circ$$

Question 17

Which of the following is the correct sum identity for $$\cos(A+B)$$?

Accepted Answer

$$\cos A \cos B - \sin A \sin B$$

Question 18

If $$	an(	heta) = -1$$ and $$	heta is in $$Quadrant IV, what is $$	heta in $$radians?

Accepted Answer

$$\frac{7\pi}{4}$$

Question 19

Find the exact value of $$\cos 25^\circ \cos 5^\circ - \sin 25^\circ \sin 5^\circ.$$

Accepted Answer

$$\cos(30^\circ)$$

Question 20

A ramp rises at an angle of $$15^\circ to $$the horizontal. If the ramp is 12 meters long, what is the vertical height?

Accepted Answer

$$12 \cdot \sin 15^\circ$$

Trigonometry Study Guide 3: Step-by-Step Guidance

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