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

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

Q: Which of the following is the correct double angle formula for $$\cos 2\theta$$?

$$\cos^2$ \theta - \sin^2$ \theta$$

Q: A building casts a shadow of 10 meters when the angle of elevation of the sun is $$37^\circ. $$What is the height of the building?

$$10 \times \tan 37^\circ = 10 \times \frac{3}{4} = 7.5$$ meters

Q: A ramp rises 3 meters vertically and runs 4 meters horizontally. What is the angle $$\theta$$ the ramp makes with the ground?

$$\theta = \arctan\left(\frac{3}{4}\right) = 37^\circ$$

Q: A surveyor measures the angle of elevation to the top of a building as $$53^\circ$$ from a point 20 meters from the base. What is the height of the building?

$$20 \times \tan 53^\circ = 20 \times \frac{4}{3} = 26.67$$ meters

Question 1

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

Accepted Answer

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

Question 2

Given $$\cos(37^\circ) = \frac{4}{5}$$, what is $$\sin(53^\circ)$$?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

If $$	an 53^\circ = \frac{4}{3}$$, what is $$	an 37^\circ$$?

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

A ladder makes an angle $$	heta$$ with the ground such that $$\sin 	heta = 0.6. $$What is $$	heta$$?

Accepted Answer

$$37^\circ$$

Question 7

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 8

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

Accepted Answer

$$\sin 	heta$$

Question 9

Which of the following is the correct double angle formula for $$\cos 2	heta$$?

Accepted Answer

$$\cos^2$ 	heta - \sin^2$ 	heta$$

Question 10

A building casts a shadow of 10 meters when the angle of elevation of the sun is $$37^\circ. $$What is the height of the building?

Accepted Answer

$$10 	imes 	an 37^\circ = 10 	imes \frac{3}{4} = 7.5$$ meters

Question 11

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

Accepted Answer

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

Question 12

If $$\sin^2$ 	heta + \cos^2$ 	heta = 1$$, what is $$\sin^2$ 37^\circ + \cos^2$ 37^\circ$$?

Accepted Answer

$$1$$

Question 13

Which of the following is the correct formula for $$\sin(180^\circ - 	heta)$$?

Accepted Answer

$$\sin 	heta$$

Question 14

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

Accepted Answer

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

Question 15

Which of the following is the correct formula for $$\cos(180^\circ - 	heta)$$?

Accepted Answer

$$-\cos 	heta$$

Question 16

A ramp rises 3 meters vertically and runs 4 meters horizontally. What is the angle $$	heta$$ the ramp makes with the ground?

Accepted Answer

$$	heta = \arctan\left(\frac{3}{4}ight) = 37^\circ$$

Question 17

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

Accepted Answer

$$1$$

Question 18

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

Accepted Answer

$$	ext{undefined}$$

Question 19

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 20

A surveyor measures the angle of elevation to the top of a building as $$53^\circ$$ from a point 20 meters from the base. What is the height of the building?

Accepted Answer

$$20 	imes 	an 53^\circ = 20 	imes \frac{4}{3} = 26.67$$ meters

Essential Trigonometric Identities and Properties

Guida di studio - Domande di pratica

Study guide - Flashcard