Free Printable RETAKE Unit 4 Part 1 ORPC

1.

Which triangle creates the angle,

\frac{5\pi}{6}

, on the Unit Circle?

a)

Equilateral triangle

b)

Isosceles non-right triangle

c)

45-45-90 triangle

d)

30-60-90 triangle

2.

$105\degree\ is\ equivalent\ to$

a)

$\frac{5\pi}{12\ }\ radians$

b)

$\frac{7\pi}{12\ }\ radians$

c)

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

d)

$\frac{8\pi}{15\ }\ radians$

3.

$Given\ \tan\theta=\frac{12}{5},\ with\ \pi<\theta<\frac{3\pi}{2},\$ determine the following. $\sin\theta=$

a)

$\frac{5}{13}$

b)

$-\frac{5}{13}$

c)

$-\frac{12}{13}$

d)

$\frac{12}{13}$

e)

$-\frac{5}{12}$

4.

$Given\ \tan\theta=\frac{12}{5},\ with\ \pi<\theta<\frac{3\pi}{2},\$ determine the following. $\sec\theta=$

a)

$\frac{13}{5}$

b)

$-\frac{13}{5}$

c)

$-\frac{13}{12}$

d)

$\frac{13}{12}$

e)

$-\frac{12}{5}$

5.

Check all true statements:

a)

$a^2+b^2=c^2$ is an identity because the equation helps create the Unit Circle.

b)

$3x+4=19\$ is an identity because the solution is x=5.

c)

$a\left(b+c\right)=ab+bc\$ is an identity because the property is always true no matter the value of the variables.

d)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ is an identity because the equation solves all quadratics regardless of what the quadratic is equal to $\left(ax^2+bx+c=R\right)$ .

e)

$\left(ax+by\right)^2=a^2x^2+2abxy+b^2y^2$ is an identity because the expansion correctly represents the expansion for all binomials.

6.

Simplify $\sec^2\theta\cdot\cot^2\theta\cdot\sin\theta$

a)

$\sin\theta$

b)

$\csc\theta$

c)

$\tan\theta$

d)

$\sec\theta$

e)

$1$

7.

Simplify $\sec\theta\cdot\csc\theta\cdot\left(1-\cos^2\theta\right)$

a)

$\sin\theta$

b)

$\csc\theta$

c)

$\tan\theta$

d)

$\sec\theta$

e)

$\cot\theta$

8.

Simplify $\cos\theta+\tan\theta\cdot\sin\theta$

a)

$\sin\theta$

b)

$\csc\theta$

c)

$\tan\theta$

d)

$\sec\theta$

e)

$\cot\theta$

9.

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

a)

$0$

b)

$\frac{1}{2}$

c)

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

d)

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

e)

$1$

10.

$\cos\left(\frac{5\pi}{6}\right)=$

a)

$0$

b)

$-\frac{1}{2}$

c)

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

d)

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

e)

$\frac{1}{2}$

11.

$\tan\left(\frac{11\pi}{6}\right)=$

a)

$0$

b)

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

c)

$-1$

d)

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

e)

$-\sqrt{3}$

12.

$\sec\left(\frac{14\pi}{3}\right)=$

a)

$1$

b)

$-2$

c)

$-\sqrt{2}$

d)

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

e)

$undefined$

13.

Solve: $\sin^2\theta-1=0\ \ \left(0\le\theta<2\pi\right)$

a)

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

b)

$\frac{\pi}{6},\ \ \frac{7\pi}{6},$

c)

$\ \frac{3\pi}{4},\ \frac{5\pi}{4}$

d)

$\frac{\pi}{3},\ \frac{5\pi}{3}$

e)

$\frac{\pi}{12},\ \frac{11\pi}{12}$

14.

Solve: $\tan\theta+\sqrt{3}=0\ \ \left(0\le\theta<2\pi\right)$

a)

$\frac{\pi}{6},\ \frac{\pi}{3}$

b)

$\frac{7\pi}{6},\ \frac{11\pi}{6}$

c)

$\frac{2\pi}{3},\ \frac{5\pi}{3}$

d)

$\frac{\pi}{6},\ \frac{7\pi}{6}$

e)

$\frac{5\pi}{3},\ \frac{5\pi}{6}$

15.

The graph of

y=\cos x

a)

b)

c)

d)

16.

The graph of

y=\tan x

a)

b)

c)

d)

17.

In the graph of $\cos x$ , the y-intercept is

a)

$0$

b)

$-1$

c)

$1$

d)

$undefined$

e)

$2$

18.

In the graph of $\cos x$ , the x-intercept is

a)

$0$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{2}$

d)

$undefined$

e)

$\pi$

19.

In the graph of $\tan x$ , an x-intercept is at

a)

$0$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{2}$

d)

$undefined$

e)

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

20.

In the graph of $\tan x$ , a vertical asymptote is at

a)

$0$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{2}$

d)

$undefined$

e)

$\pi$

RETAKE Unit 4 Part 1 ORPC

Total questions: 20

Worksheet time: 2hrs 40mins

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