Trigonometry

Chapter 1

100

What does the Pythagorean Theorem say 

and 

on what kind of triangle can we apply it? 

Pythagorean Theorem 

a²+b²=c²

We can only use it on RIGHT triangles. 

200

Convert the radian measure to degree measure. DO not use calculator.

(5pi)/3

300^\circ

300

Find two positive and two negative angles using radian measure that are coterminal with 

\pi/6

1.

(13\pi)/6

 

2.

(25\pi)/6

3.

-(11\pi)/6

4. 

-(23\pi)/6

400

Find the exact value of tan x if cos x=-(2/3) and x is not in quadrant III.  

tan x=(-\sqrt(5))/2

500

Assume x is an angle in standard position. 

Find the quadrant in which x lies if you know that 

sin x >0 and sec x <0 

Quadrant II

Chapter 2

100

Draw one period/ one cycle of the graph 

y=- sin x

200

Draw one period/ one cycle of the graph y=sec(x).

300

Which of the following equations will shift y=cos(x) 

1. 3 units up          2. Amplitude is 2    

 3. Reflect it about the x-axis    

4.  to the right  

pi/6

y=-2cos(x-pi/6)+3

400

Write an equation of the form y=Asin[B(x-C)]+D whose graph is the given sine wave. 

y=2sin(2x)

500

Graph one cycle of y=tan(x) 

Period:

Domain: 

Range: 

Asymptotes: 

Period: 

pi

Domain: 

(-pi/2,pi/2)

Range: 

(-\infty,\infty)

Asymptotes: 

x=-pi/2, x=pi/2

Graph: 

Chapter 3

100

Write each expression in terms of sines and/or cosines, and then simplify.

tan x/secx

sin x

200

Simplify each expression. 

(1+sin(\alpha))(1+sin(-\alpha))

cos^2(\alpha)

300

Verify the identity. 

1+sec x sin x tan x = sec^2 x

400

Prove the identity. 

sin(-t)cos(2t)-cos(-t)sin(-2t) = sin t

500

Prove the identity. 

2sin^2(x/2)=sin^2 x/(1+cos x)

use 

sin (x/2)=\pm \sqrt((1-cos x)/2)

Chapter 4

100

Graph 

y=tan^{-1}(x)

Domain: 

Range

Domain: 

(-infty,\infty)

Range: 

(-pi/2,pi/2)

Graph: 

200

Find the exact value of each expression without using a calculator or table. 

a. 

sin^{-1}(1/sqrt2)

b. 

arcsin(1)

c. 

cos^{-1}(-\sqrt3/2)

a. 

pi/4

b.

pi/2

c.

(5pi)/6

300

Find all solutions, in degrees or radians: 

tan \alpha=1 

Degrees: 

{\alpha|\alpha= 45^\circ+k180^\circ}

Radians: 

{\alpha|\alpha=pi/4+pik}

400

Find the inverse of the function and state the domain and range of inverse function. 

f(x)=1+tan(pi/2x)  -1<x<1

Domain:

(-infty,infty)

 

Range:

(-1,1)

f^{-1}(x)=2/pitan^{-1}(x-1) 

500

Find all solutions to the equation in the interval 

[0,2pi]

sin(2x)+sin(pi/2-x)=0

{(7pi)/6,(11pi)/6,pi/2,(3pi)/2}

Chapter 5

100

Determine the number of triangles with the given parts and solve the triangle. 

\alpha=39.6^\circ,c=18.4, a=3.7

none

200

x=18.1 inches

300

Solve the triangle. Round to the nearest tenth. 

\alpha=30.4^circ, beta=28.3^circ,c=5.2

400

Let r=<3,-2> and t=<4,-6> 

Find 2r+3t and write vectors in the form <a,b>

<18,-22>

500

Prove the law of sines. 

Chapter 6

100

Perform the indicated operations with the complex numbers. 

a. 

(-2+3i)+(-4-9i)

b. 

2i(3+i)

c. 

(-3i)^2

a.

-6-6i

b.

-2+6i

c.

-9

200

Write the complex number in trigonometric form, using degree measure for the argument. 

-\sqrt3+i

2(cos 150^\circ+isin 150^circ)

300

For the polar equation, write an equivalent rectangular equation. 

r=1/(sin theta+cos theta)

x+y=1

400

Simplify each expression, by using trigonometric form and DeMoivre's theorem. 

(\sqrt3-i)^4

-8-8i\sqrt3

500

Find all complex solutions to the equation. express answers in the form a+bi. 

ix^2+3=0

\sqrt6/2+\sqrt6/2i, -\sqrt6/2-\sqrt6/2i,