Free Printable Week 6: Check for Understanding

1.

The angle shown is in standard position. Select the possible measures of the angle.

a)

$-450\degree$

b)

$-360\degree$

c)

$-270\degree$

d)

$-90\degree$

e)

$270\degree$

2.

An angle whose measure is $405\degree$ is in standard position. In what quadrant does the terminal side of the angle fall?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

3.

An angle measures $\frac{7}{9}\pi$ radians. What is the degree measure of the angle?

a)

$2.44\degree$

b)

$140\degree$

c)

$280\degree$

d)

$439.6\degree$

4.

How many radians is $-135\degree$ ?

a)

$-\frac{1}{4}\pi$

b)

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

c)

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

d)

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

5.

A circle has a radius of 10 inches. Find the approximate length of the arc intersected by a central angle of $\frac{2\pi}{3}$ .

a)

6.67 inches

b)

10.47 inches

c)

20.94 inches

d)

62.8 inches

6.

Find the coordinates of the point (x, y) shown on the unit circle. $y=?$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

$\frac{\sqrt{3}}{2}$

7.

Identify the reference angle $\phi$ for the given angle, $\theta.$

When $\theta=300\degree,\ \phi=?\degree$

(a)

8.

Identify the reference angle $\phi$ for the given angle, $\theta.$

When $\theta=-210\degree,\ \phi=?\degree$

(a)

9.

Select all the angle measures for which $\cos\theta=\frac{1}{2}$

a)

$-120\degree$

b)

$-60\degree$

c)

$120\degree$

d)

$600\degree$

e)

$660\degree$

10.

The point $\left(-7,\ -24\right)$ is on the terminal ray of the angle $\theta$ which is in standard position. A student found the six trigonometric values for angle $\theta$ . The student's answers are shown. Which value(s) are incorrect?
$\sin\theta=\frac{24}{25}$ $\csc\theta=\frac{25}{24}$
$\cos\theta=-\frac{7}{25}$ $\sec\theta=-\frac{25}{7}$
$\tan\theta=-\frac{24}{7}$ $\cot\theta=-\frac{7}{24}$

a)

$\sin\theta$

b)

$\cos\theta$

c)

$\tan\theta$

d)

$\csc\theta$

e)

$\cot\theta$

11.

Angle $\theta$ is in standard position. If $\sin\theta=-\frac{1}{3}$ , and $\pi<\theta<\frac{3\pi}{2}$ , find $\cos\theta$ .

a)

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

b)

$-\frac{4}{3}$

c)

$\frac{4}{3}$

d)

$\frac{2\sqrt{2}}{3}$

12.

The period of the function is $4\pi$ . How many cycles of the function occur in a horizontal length of $12\pi$ ?

(a)

13.

Which type of transformation of the parent function would be shown by the graph?

a)

vertical stretch

b)

horizontal stretch

c)

vertical compression (shrink)

d)

horizontal compression (shrink)

e)

horizontal shift

14.

Which could be the equation for the function shown in the graph?

a)

$y=\sin\left(x-\frac{3\pi}{2}\right)$

b)

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

c)

$y=\sin\left(x-\frac{\pi}{4}\right)$

15.

Transform $y=\cot\left(x\right)$ to get the graph of $y=3\cot\left(\frac{1}{5}\left(x+2\right)\right)$ . Which type of transformation is NOT performed?

a)

vertical shift

b)

horizontal shift

c)

vertical stretch

d)

horizontal stretch

16.

The graph of $y=\tan\left(\frac{1}{4}\left(x-\frac{\pi}{2}\right)\right)+1$ is shown. What is the period of the function?

a)

$\pi$

b)

$\frac{5\pi}{2}$

c)

$4\pi$

d)

$2\pi$

17.

How do you translate the graph of $f\left(x\right)=x^3$ left 4 units and down 2 units? Identify the equation of the graph.

a)

$y=\left(x+4\right)^3-2$

b)

$y=\left(x-4\right)^3-2$

c)

$y=\left(x+2\right)^3-4$

d)

$y=\left(x-2\right)^3-4$

18.

Given that $f\left(x\right)$ is the original function, what is true about the transformation, $g\left(x\right)$ ?

a)

$g\left(x\right)$ is reflected about the y- axis.

b)

$g\left(x\right)$ is reflected about the y-axis and shifted up by 4 units.

c)

$g\left(x\right)$ is reflected about the x-axis.

d)

$g\left(x\right)$ is reflected about the x-axis and shifted up by 4 units.

Week 6: Check for Understanding

Total questions: 18

Worksheet time: 2hrs 40mins

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