Quiz about PCT - Trig Graphs Review

Question 1

Which statement is NOT true for the function f given by $$f\left( heta ight)=\sin\left( heta ight)$$ , for values of $$ heta$$ between 0 and $$2\pi$$ ?

Accepted Answer

$$\sin\left( heta ight)=0$$ only when $$ heta=0$$

Answer

The range of the function is from -1 to 1

Answer

$$\sin\left( heta ight)=1$$ only when $$ heta=\frac{\pi}{2}$$

Answer

$$\sin\left( heta ight)>0$$ for $$0< heta<\pi$$

Question 2

Angle $$ heta$$ , measured in radians, satisfies $$\cos\left( heta ight)=0$$ . What could the value of $$ heta$$ be? Select ALL the answers that apply.

Accepted Answer

$$\frac{\pi}{2}$$

Accepted Answer

$$\frac{3\pi}{2}$$

Answer

$$0$$

Answer

$$\frac{\pi}{4}$$

Answer

$$\pi$$

Question 3

Which statements are true for BOTH functions $$y=\sin\left( heta ight)$$ and $$y=\cos\left( heta ight)$$ ? Select ALL that apply.

Accepted Answer

The period is $$2\pi$$

Accepted Answer

The maximum value is 1

Accepted Answer

The function has a value of $$\frac{\sqrt[]{2}}{2}$$ when $$ heta=\frac{\pi}{4}$$ .

Answer

The maximum value occurs at $$ heta=0$$

Answer

The minimum value is 0.

Question 4

For which of these angles is the sine negative? Select ALL that apply.

Accepted Answer

$$-\frac{\pi}{4}$$

Accepted Answer

$$-\frac{\pi}{3}$$

Accepted Answer

$$-\frac{2\pi}{3}$$

Answer

$$-\frac{4\pi}{3}$$

Answer

$$-\frac{11\pi}{6}$$

Question 5

Which of these statements are true about the function f given by $$f\left( heta ight)=\sin\left( heta ight)$$ ? Select ALL that apply.

Accepted Answer

The graph crosses the x-axis at $$0,\pm\pi,\pm2\pi,...$$

Accepted Answer

The value of y always stays the same when $$2\pi$$ radians is added to the input

Accepted Answer

The value of y always stays the same when $$-2\pi$$ radians is added to the input

Accepted Answer

The graph has a maximum at $$ heta=\frac{5\pi}{2}$$ .

Answer

The value of y always stays the same when $$\pi$$ radians is added to the input

Question 6

In which quadrant are both the sine and the tangent negative?

Accepted Answer

4th

Answer

1st

Answer

2nd

Answer

3rd

Question 7

The function f is given by $$f\left( heta ight)= an\left( heta ight)$$ . Which of the statements are true? Select ALL that apply.

Accepted Answer

The range of f is all real numbers

Accepted Answer

The period of f is $$\pi$$

Answer

The domain of f is all real numbers

Answer

The period of f is $$2\pi$$

Question 8

Select ALL trigonometric functions with an amplitude of 3.

Accepted Answer

$$y=3\sin\left(x\right)+1$$

Accepted Answer

$$y=3\cos\left(x\right)+2$$

Accepted Answer

$$y=3\sin\left(x\right)$$

Answer

$$y=\sin\left(x\right)+3$$

Answer

$$y=\cos\left(3x\right)$$

Question 9

Which expression value is the same as $$\cos\left( heta ight)$$ when $$ heta=0,\ \frac{\pi}{2},\ \pi,\ and\ \frac{3\pi}{2}$$ ?

Accepted Answer

$$\sin\left( heta+\frac{\pi}{2} ight)$$

Answer

$$\sin\left( heta-\frac{\pi}{2} ight)$$

Answer

$$\sin\left( heta-\pi ight)$$

Answer

$$\sin\left( heta+\pi ight)$$

Question 10

What trigonometric equation does the graph represent?

Accepted Answer

$$y=2\cos\left( heta-\frac{\pi}{4} ight)$$

Answer

$$y=2\sin\left( heta ight)$$

Answer

$$y=2\cos\left( heta+\frac{\pi}{4} ight)$$

Answer

$$y=2\sin\left( heta-\frac{\pi}{4} ight)$$

Question 11

Select ALL the functions that have a period of $$\pi$$ .

Accepted Answer

$$y= an\left(x ight)$$

Accepted Answer

$$y=\cos\left(2x\right)$$

Accepted Answer

$$y=\sin\left(2x\right)$$

Answer

$$y=\cos\left(\frac{x}{2}\right)$$

Answer

$$y=\sin\left(\frac{x}{2}\right)$$

Question 12

Which function has an amplitude of 5?

Accepted Answer

$$y=5\sin\left(x\right)$$

Answer

$$y=\sin\left(5x\right)$$

Answer

$$y=\sin\left(x+5\right)$$

Answer

$$y=\sin\left(x\right)+5$$

Question 13

Which of these is true for the function $$y=3\sin\left(\frac{x}{2}\right)$$ ?

Accepted Answer

Period is $$4\pi$$

Answer

Period is $$\pi$$

Answer

Period is 3

Answer

Period is $$2\pi$$

PCT - Trig Graphs Review

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