Q: Solve for $$\theta$$: $$\sin(3\theta - 17^\circ) = \cos(\theta + 43^\circ).$$

$$3\theta - 17^\circ = 90^\circ - (\theta + 43^\circ)$$

Q: Verify the identity: $$\tan(x - \dfrac{\pi}{4}) = \dfrac{\tan x - 1}{1 + \tan x}. $$Which of the following is a correct step?

$$\tan(x - \dfrac{\pi}{4}) = \dfrac{\tan x - \tan \dfrac{\pi}{4}}{1 + \tan x \tan \dfrac{\pi}{4}}$$

Question 1

Use the sum-to-product identity to simplify the expression $$\cos 36^\circ \cos 24^\circ - \sin 36^\circ \sin 24^\circ.$$

Accepted Answer

$$\cos(60^\circ)$$

Question 2

Given $$\cos s = \dfrac{1}{3}$$ with $$s in $$Quadrant I, and $$\sin t = -\dfrac{1}{2}$$ with $$t in $$Quadrant IV, find $$\cos(s + t).$$

Accepted Answer

$$\dfrac{5}{6}$$

Question 3

Write $$\cos(	heta + 270^\circ) as a $$function of $$	heta.$$

Accepted Answer

$$-\sin 	heta$$

Question 4

Find $$\sin(s - t)$$ given $$\cos s = \dfrac{1}{3}$$ with $$s in $$Quadrant I, and $$\sin t = -\dfrac{1}{2}$$ with $$t in $$Quadrant IV.

Accepted Answer

$$\dfrac{1}{6}$$

Question 5

Express $$\sin 61^\circ as a $$cofunction of a complementary angle.

Accepted Answer

$$\cos 29^\circ$$

Question 6

Solve for $$	heta$$: $$\sin(3	heta - 17^\circ) = \cos(	heta + 43^\circ).$$

Accepted Answer

$$3	heta - 17^\circ = 90^\circ - (	heta + 43^\circ)$$

Question 7

Verify the identity: $$\cos\left(\dfrac{3\pi}{2} - x\right) = -\sin x. $$Which of the following steps is correct?

Accepted Answer

$$\cos\left(\dfrac{3\pi}{2} - x\right) = \sin(x - \dfrac{3\pi}{2}) = -\sin x$$

Question 8

Find the exact value of $$	an 75^\circ$$ using sum or difference identities.

Accepted Answer

$$2 + \sqrt{3}$$

Question 9

Express $$\sin(x - \dfrac{\pi}{2}) as a $$function of $$x.$$

Accepted Answer

$$-\cos x$$

Question 10

Given $$\cos 2	heta = \dfrac{1}{4}$$ and $$	heta is in $$Quadrant III, find $$\cos 	heta.$$

Accepted Answer

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

Question 11

If $$	an 	heta = \dfrac{7}{24}$$ and $$\sin 	heta \u003c 0$$, find $$\cos 2	heta.$$

Accepted Answer

$$\dfrac{527}{625}$$

Question 12

Simplify $$\cos^2$ 4x - \sin^2$ 4x$$ using a double angle identity.

Accepted Answer

$$\cos 8x$$

Question 13

Given $$\cos s = -\dfrac{5}{13}$$ with $$s in $$Quadrant II, and $$\sin t = \dfrac{15}{17}$$ with $$t in $$Quadrant II, find $$\cos(s - t). $$

Accepted Answer

$$\dfrac{56}{221}$$

Question 14

Use the sum or difference identity to find the exact value of $$\sin\left(\dfrac{7\pi}{12}\right). $$

Accepted Answer

$$\dfrac{\sqrt{6} + \sqrt{2}}{4}$$

Question 15

Simplify $$4\sin 2x \cos 2x$$ using a double angle identity.

Accepted Answer

$$2\sin 4x$$

Question 16

If $$\cos 	heta = \dfrac{5}{13}$$ and $$\sin 	heta \u003c 0$$, find $$\sin 2	heta.$$

Accepted Answer

$$-\dfrac{120}{169}$$

Question 17

Use the sum or difference identity to find the exact value of $$\sin 15^\circ \cos 105^\circ + \cos 15^\circ \sin 105^\circ.$$

Accepted Answer

$$\sin 120^\circ$$

Question 18

Simplify $$2	an 15^\circ / (1 - 	an^2$ 15^\circ)$$ using a double angle identity.

Accepted Answer

$$	an 30^\circ$$

Question 19

Verify the identity: $$	an(x - \dfrac{\pi}{4}) = \dfrac{	an x - 1}{1 + 	an x}. $$Which of the following is a correct step?

Accepted Answer

$$	an(x - \dfrac{\pi}{4}) = \dfrac{	an x - 	an \dfrac{\pi}{4}}{1 + 	an x 	an \dfrac{\pi}{4}}$$

Question 20

A ladder leans against a wall making an angle of $$75^\circ$$ with the ground. If the foot of the ladder is 2 meters from the wall, how high up the wall does the ladder reach? (Use $$	an 75^\circ = 2 + \sqrt{3})$$

Accepted Answer

$$2(2 + \sqrt{3})$$ meters

Trigonometry Chapter 5 Quiz 2 – Step-by-Step Guidance

Guida di studio - Domande di pratica

Study guide - Flashcard