$$\tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$$

$$\cos^2$ \theta = \cos^2$ \theta - \sin^2$ \theta + 2 \sin \theta \cos \theta - 1$$

$$4 \times \tan 53^\circ = 4 \times \frac{4}{3} = \frac{16}{3}$$ meters

Question 1

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

Accepted Answer

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

Question 2

What is the value of $$\cos 53^\circ$$?

Accepted Answer

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

Question 3

Which trigonometric identity correctly expresses $$\sin(A+B)$$?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

Question 4

A ladder makes an angle of $$37^\circ$$ with the ground. If the length of the ladder is 5 meters, what is the height it reaches on the wall?

Accepted Answer

$$3$$ meters

Question 5

Which formula represents $$	an(A+B)$$?

Accepted Answer

$$	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B}$$

Question 6

If $$\sin 	heta = \frac{3}{5}$$, what is $$\cos 	heta$$?

Accepted Answer

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

Question 7

Which equation is used to convert logarithms from base $$e to $$base $$10$$?

Accepted Answer

$$\log_e x = 2.303 \log_{10} x$$

Question 8

What is the value of $$	an 53^\circ$$?

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Which formula represents $$\cos(A+B)$$?

Accepted Answer

$$\cos(A+B) = \cos A \cos B - \sin A \sin B$$

Question 12

A ramp is inclined at $$37^\circ to $$the horizontal. If the horizontal distance is 4 meters, what is the length of the ramp?

Accepted Answer

$$5$$ meters

Question 13

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

Accepted Answer

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

Question 14

If $$\cos 	heta = \frac{3}{5}$$, what is $$	an 	heta$$?

Accepted Answer

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

Question 15

Which equation is used to convert logarithms from base $$10 to $$base $$e$$?

Accepted Answer

$$\log_{10} x = \frac{1}{2.303} \log_e x$$

Question 16

If $$\sin 	heta = \frac{4}{5}$$, what is $$	an 	heta$$?

Accepted Answer

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

Question 17

Which trigonometric identity is used to express $$\cos^2$ 	heta in $$terms of $$\cos 	heta$$?

Accepted Answer

$$\cos^2$ 	heta = \cos^2$ 	heta - \sin^2$ 	heta + 2 \sin 	heta \cos 	heta - 1$$

Question 18

A building casts a shadow of 4 meters when the angle of elevation of the sun is $$53^\circ. $$What is the height of the building?

Accepted Answer

$$4 	imes 	an 53^\circ = 4 	imes \frac{4}{3} = \frac{16}{3}$$ meters

Question 19

Which formula represents $$\cos(180^\circ - 	heta)$$?

Accepted Answer

$$-\cos 	heta$$

Question 20

If $$\sin 	heta = \frac{3}{5}$$, what is $$	an 	heta$$?

Accepted Answer

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

Core Trigonometric Identities and Graphs: A Study Guide

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