Quiz about 9.1 Reference Triangles & Inverse Trig Functions

Question 1

Given the triangle, what is $$\csc heta$$ ?

Accepted Answer

$$\sqrt[]{2}$$

Answer

$$\frac{\sqrt[]{2}}{2}$$

Answer

1

Answer

$$\frac{\sqrt[]{2}}{23}$$

Question 2

Given the triangle, what is $$\sec heta$$ ?

Accepted Answer

$$\frac{13\sqrt[]{5}}{22}$$

Answer

$$\frac{22\sqrt[]{5}}{65}$$

Answer

$$\frac{13\sqrt[]{5}}{19}$$

Answer

$$\frac{19\sqrt[]{5}}{65}$$

Question 3

Given the triangle, what is $$\cot heta$$ ?

Accepted Answer

$$\frac{22}{19}$$

Answer

$$\frac{22\sqrt[]{5}}{65}$$

Answer

$$\frac{19}{22}$$

Answer

$$\frac{19\sqrt[]{5}}{65}$$

Question 4

Which of the following statements is true about this right triangle? (Select all that apply) (Hint: you might need to find some trig ratios)

Accepted Answer

$$\sin heta=\cos heta$$

Accepted Answer

$$ an heta=\cot heta$$

Answer

$$\sin heta=\csc heta$$

Answer

$$\cos heta=\sec heta$$

Question 5

Using the given point on the terminal side of the angle $$ heta$$ , what is $$ an\ heta$$ ?

Accepted Answer

$$ an heta=-\frac{7}{12}$$

Answer

$$ an heta=-\frac{12}{7}$$

Answer

$$ an heta=-\frac{12\sqrt[]{193}}{193}$$

Answer

$$ an heta\pm-\frac{7\sqrt[]{193}}{7}$$

Question 6

Draw a reference triangle through the point $$\left(2,\sqrt[]{5} ight)$$ . Then find the value of $$\sin\ heta$$ .

Accepted Answer

$$\sin heta=\frac{\sqrt[]{5}}{3}$$

Answer

$$\sin heta=\frac{3\sqrt[]{5}}{5}$$

Answer

$$\sin\ heta=\frac{\sqrt[]{5}}{2}$$

Answer

$$\sin heta=\frac{2\sqrt[]{5}}{5}$$

Question 7

Draw a reference triangle through the point (-4, 3) . Then find the value of $$\csc heta$$ .

Accepted Answer

$$\csc heta=\frac{5}{3}$$

Answer

$$\csc heta=\frac{-4}{5}$$

Answer

$$\csc heta=\frac{\sqrt[]{7}}{3}$$

Answer

$$\csc heta=\frac{4\sqrt[]{7}}{7}$$

Question 8

If the $$\sin heta>0$$ , which of the following statements *must* also be true?

Accepted Answer

$$\csc heta>0$$

Answer

$$\cos\ heta>0$$

Answer

$$ an heta>0$$

Answer

$$ heta$$ is definitely in Quadrant II.

Question 9

Let $$ heta$$ be an angle in standard position. In what quadrant(s) can $$ heta$$ lie if $$\sin heta$$ and $$\cos heta$$ have opposite signs? (Select all that apply)

Accepted Answer

Quadrant II

Accepted Answer

Quadrant IV

Answer

Quadrant I

Answer

Quadrant III

Question 10

Let $$ heta$$ be an angle in standard position. In what quadrant(s) can $$ heta$$ if $$\cos heta<0$$ and $$ an\ heta>0$$ ?

Accepted Answer

Quadrant III

Answer

Quadrant I

Answer

Quadrant II

Answer

Quadrant IV

Question 11

Given $$\csc heta=\frac{5}{4}$$ where $$\frac{\pi}{2}< heta<\pi$$ , what is $$ an heta$$ ?

(Hint: draw a reference triangle)

Accepted Answer

$$ an heta=-\frac{4}{3}$$

Answer

$$ an heta=-\frac{3}{4}$$

Answer

$$ an heta=-\frac{5}{3}$$

Answer

$$ an heta=-\frac{3}{5}$$

Question 12

In what quadrant all are the trig ratios positive?

Accepted Answer

Quadrant I

Answer

Quadrant II

Answer

Quadrant III

Answer

Quadrant IV

Question 13

Given the triangle, what is $$\sec heta$$ ?

Accepted Answer

$$\frac{\sqrt[]{5}}{2}$$

Answer

$$\frac{2\sqrt[]{5}}{5}$$

Answer

$$\sqrt[]{5}$$

Answer

$$\frac{\sqrt[]{5}}{5}$$

9.1 Reference Triangles & Inverse Trig Functions

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