Q: Which of the following identities is always true for all values of $$\theta$$?

$$\sin^2$(\theta) + \cos^2$(\theta) = 1$$

Q: Which of the following is the correct expression for $$\tan(\alpha + \beta)$$?

$$\frac{\tan(\alpha) + \tan(\beta)}{1 - \tan(\alpha)\tan(\beta)}$$

Question 1

Given the equation $$	an(	heta) = \frac{\sin(	heta)}{\cos(	heta)}$$, which of the following is the correct value for $$	an(45^\circ)$$?

Accepted Answer

$$1$$

Question 2

If $$	an(	heta) = \frac{3}{4}$$ and $$	heta is in $$the first quadrant, what is $$\sin(	heta)$$?

Accepted Answer

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

Question 3

Which of the following identities is always true for all values of $$	heta$$?

Accepted Answer

$$\sin^2$(	heta) + \cos^2$(	heta) = 1$$

Question 4

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the ladder is 10 ft long and the angle is $$60^\circ$$, what is the height the ladder reaches on the wall?

Accepted Answer

$$10 \sin(60^\circ)$$

Question 5

If $$\sin(	heta) = \frac{5}{13}$$ and $$	heta is in $$the first quadrant, what is $$\cos(	heta)$$?

Accepted Answer

$$\frac{12}{13}$$

Question 6

Which of the following is the correct expression for $$	an(\alpha + \beta)$$?

Accepted Answer

$$\frac{	an(\alpha) + 	an(\beta)}{1 - 	an(\alpha)	an(\beta)}$$

Question 7

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

Accepted Answer

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

Question 8

If $$	an(	heta) = -1$$ and $$	heta is $$between $$180^\circ$$ and $$270^\circ$$, what is $$	heta$$?

Accepted Answer

$$225^\circ$$

Question 9

Which of the following is equivalent to $$\frac{1}{\cos(	heta)}$$?

Accepted Answer

$$\sec(	heta)$$

Question 10

If $$\sin(	heta) = 0.6$$ and $$	heta is in $$the second quadrant, what is $$\cos(	heta)$$?

Accepted Answer

$$-0.8$$

Question 11

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

Accepted Answer

$$20 	an(30^\circ)$$

Question 12

Which of the following is the correct value for $$\sin(90^\circ)$$?

Accepted Answer

$$1$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following is the correct double angle formula for $$\sin(2	heta)$$?

Accepted Answer

$$2\sin(	heta)\cos(	heta)$$

Solving Quadratic Equations by the Quadratic Formula

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