Trigonometry, Quadrantal and Reference Angles

​4.4 Trigonometric Functions of Any Angle

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Multiple Choice

Point P(7, -24) is a point on the terminal side of the angle $$\theta$$ . Find the exact value of sine $$\theta$$ .

#1

• $$-\frac{24}{25}$$  

• $$\frac{7}{25}$$  

• $$-\frac{24}{7}$$  

• $$\frac{24}{25}$$  

Multiple Choice

Point Q(-5, -12) is a point on the terminal side of the angle $$\theta$$ . Find the exact value of cosine $$\theta$$ . #3

• $$\frac{5}{13}$$  

• $$-\frac{12}{13}$$  

• $$-\frac{5}{13}$$  

• $$-\frac{13}{5}$$  

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Multiple Choice

Given that $$\theta$$ is an angle in standard form. In which quadrant does  $$\sin\theta<0,\ \cos\theta>0$$  lie? #5

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

Given that $$\theta$$ is an angle in standard form. In which quadrant does  $$\tan\theta<0,\ \cos\theta<0$$  lie? #6

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

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Multiple Choice

What is the reference angle for $$172\degree$$  ? #8

• $$8\degree$$  

• $$16\degree$$  

• $$18\degree$$  

• $$72\degree$$  

Multiple Choice

What is the reference angle for $$\frac{5\pi}{4}$$ ? #9

• $$\frac{3\pi}{4}$$  

• $$\frac{\pi}{3}$$  

• $$\frac{\pi}{2}$$  

• $$\frac{\pi}{4}$$  

Multiple Choice

In what quadrant can you find the angle $$210\degree$$  ? #15

• QI

• QII

• QIII

• QIV

Fill in the Blanks

What is the reference angle of $210\degree$  ? #16

Multiple Choice

sinθ = 3/5 ; θ lies in Quadrant II. What are the other 5 trigonometric functions? #18

• cosθ = 4/5 ; tanθ = 3/4 ; cscθ = 5/3 ; secθ = 5/4 ; cotθ = − 4/3

• cosθ = − 4/5 ; tanθ = − 3/4 ; cscθ = 5/3 ; secθ = − 5/4 ; cotθ = − 4/3

• cosθ = 5/4 ; tanθ = 3/4 ; cscθ = 3/5 ; secθ = 5/4 ; cotθ = − 4/3

• cosθ = − 5/4 ; tanθ = − 3/4 ; cscθ = 3/5 ; secθ = − 5/4 ; cotθ = − 4/3

Multiple Choice

sinθ = 0; secθ = −1 What are the other 5 trigonometric functions? #19

• sinθ = 0; cosθ = −1; tanθ = 0; cscθ is undefined; secθ = −1; cotθ is undefined

• sinθ = 0; cosθ = 1; tanθ = 0; cscθ is undefined; secθ = 1; cotθ is undefined

• sinθ = 0; cosθ = −1; tanθ = 0; cscθ is undefined; secθ = 1; cotθ is undefined

• sinθ = 0; cosθ = 1; tanθ = 0; cscθ is undefined; secθ = −1; cotθ is undefined

Multiple Choice

If  $$\sin\theta\ =\frac{3}{5}$$  and  $$\frac{\pi}{2}\le\theta\le\frac{3\pi}{2}$$ , find  $$\cos\theta$$  . #27

• $$\frac{4}{5}$$  

• $$-\frac{4}{5}$$  

• $$\frac{3}{4}$$  

• $$-\frac{3}{4}$$  

Multiple Choice

$$\sin225\degree$$  =_______ #28

•   $$\frac{1}{2}$$  

• $$-\frac{1}{2}$$  

• $$\frac{1}{\sqrt{2}}$$  

• $$-\frac{1}{\sqrt{2}}$$  

Multiple Choice

What is the reference angle? #23

• 163

• 73

• 27

• 107

Multiple Choice

Which of the following is a correct representation of the reference angle of $$\theta=210\degree$$  . #24

Multiple Choice

What is the reference angle for 275°? #42

• 85°

• 95°

• -85°

• -95°