Q: A ramp rises $$3$$ meters over a horizontal distance of $$4$$ meters. What is the angle of elevation $$\theta of $$the ramp with respect to the ground?

$$\theta = \arctan\left(\frac{3}{4}\right)$$

Question 1

Which of the following is the correct value for $$\sin 37^\circ$$?

Accepted Answer

$$\frac{3}{5}$$

Question 2

Given $$	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$$, what is $$	an(45^\circ + 45^\circ)$$?

Accepted Answer

$$	ext{undefined}$$

Question 3

If $$\cos(180^\circ - 	heta) = -\cos 	heta$$, what is $$\cos(180^\circ - 60^\circ)$$?

Accepted Answer

$$-\cos 60^\circ$$

Question 4

Which of the following is the correct expansion for $$\sin(A+B)$$?

Accepted Answer

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

Question 5

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the height reached by the ladder is $$h$$ and the length of the ladder is $$L$$, which trigonometric ratio relates $$h$$ and $$L$$?

Accepted Answer

$$\sin 	heta = \frac{h}{L}$$

Question 6

If $$\cos^2$ 	heta + \sin^2$ 	heta = 1$$, what is $$\sin^2$ 45^\circ + \cos^2$ 45^\circ$$?

Accepted Answer

$$1$$

Question 7

Which of the following is the correct value for $$	an 53^\circ$$?

Accepted Answer

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

Question 8

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos 	heta$$?

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

A ramp rises $$3$$ meters over a horizontal distance of $$4$$ meters. What is the angle of elevation $$	heta of $$the ramp with respect to the ground?

Accepted Answer

$$	heta = \arctan\left(\frac{3}{4}ight)$$

Question 11

If $$\sin(90^\circ - 	heta) = \cos 	heta$$, what is $$\sin(90^\circ - 30^\circ)$$?

Accepted Answer

$$\cos 30^\circ$$

Question 12

Which of the following is the correct value for $$\cos 53^\circ$$?

Accepted Answer

$$\frac{3}{5}$$

Question 13

If $$	an 	heta = \frac{3}{4}$$, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{3}{5}$$

Question 14

Which of the following is the correct value for $$\sin 53^\circ$$?

Accepted Answer

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

Question 15

If $$\cos(90^\circ - 	heta) = \sin 	heta$$, what is $$\cos(90^\circ - 60^\circ)$$?

Accepted Answer

$$\sin 60^\circ$$

Question 16

A building casts a shadow of $$20$$ meters when the angle of elevation of the sun is $$30^\circ. $$What is the height of the building?

Accepted Answer

$$20 	an 30^\circ$$

Question 17

Which of the following is the correct value for $$\cos 37^\circ$$?

Accepted Answer

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

Question 18

If $$	an(90^\circ - 	heta) = \cot 	heta$$, what is $$	an(90^\circ - 45^\circ)$$?

Accepted Answer

$$1$$

Question 19

Which of the following is the correct value for $$	an 37^\circ$$?

Accepted Answer

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

Question 20

If $$\sin^2$ 	heta + \cos^2$ 	heta = 1$$, what is $$\sin^2$ 60^\circ + \cos^2$ 60^\circ$$?

Accepted Answer

$$1$$

Essential Trigonometric Identities, Formulas, and Graphs

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