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

$$\frac{\tan A + \tan B}{1 - \tan A \tan B}$$

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?

$$\theta = \tan$$^{-1}$$\left(\frac{3}{4}\right)$$

Question 1

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

Accepted Answer

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

Question 2

Given $$\cos(90^\circ - 	heta)$$, which trigonometric function does it equal?

Accepted Answer

$$\sin 	heta$$

Question 3

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

Accepted Answer

$$\frac{	an A + 	an B}{1 - 	an A 	an B}$$

Question 4

If $$\cos 53^\circ = \frac{3}{5}$$, what is $$\sin 53^\circ$$?

Accepted Answer

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

Question 5

Which of the following is the correct expansion for $$\cos^2$ 	heta$$?

Accepted Answer

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

Question 6

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the height reached by the ladder is $$h$$ and the base distance is $$b$$, which trigonometric ratio is used to find $$	heta$$?

Accepted Answer

$$	an 	heta = \frac{h}{b}$$

Question 7

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

Accepted Answer

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

Question 8

If $$\sin(A+B) = \sin A \cos B + \cos A \sin B$$, what is $$\sin(60^\circ + 30^\circ)$$?

Accepted Answer

$$1$$

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

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

Accepted Answer

$$-\cos 60^\circ$$

Question 11

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

$$	heta = 	an$$^{-1}$$\left(\frac{3}{4}ight)$$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$$1$$

Question 14

Which of the following is the correct formula for $$\cos^2$ 	heta in $$terms of $$\cos 2	heta$$?

Accepted Answer

$$\frac{1 + \cos 2	heta}{2}$$

Question 15

A building casts a shadow of $$20$$ meters when the angle of elevation of the sun is $$37^\circ. $$What is the height of the building?

Accepted Answer

$$20 	an 37^\circ$$

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

$$\cos 30^\circ$$

Question 18

Which of the following is the correct formula for $$\sin^2$ 	heta in $$terms of $$\cos 2	heta$$?

Accepted Answer

$$\frac{1 - \cos 2	heta}{2}$$

Question 19

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

Accepted Answer

Undefined

Essential Trigonometric Identities and Properties

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