Trigonometry Review

Right Triangle Trig

100

State the Pythagorean Theorem

a² + b² = c² 

200

State the six trig functions

Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent

300

What are the values of the three special angles?

30^o, 45^o, 60^o

400

For a right triangle with opp = 3 and hyp = 9, find the adj side length. Give exact answer.

3*sqrt(10)

Bonus: What is the value of cos(theta)?

500

The steepest railway in the world makes an angle of about 52^o with the ground. The railway extends horizontally about 458 feet. What is the height of the railway?

about 586 feet

Angles

100

Convert 2pi radians to degrees

360^o

200

Convert -150^o to radians

-5pi/6

300

Find a negative angle coterminal with 460^o

-260^o

400

Find the reference angle for -220^o

40^o

500

The winning shot of the men's shot put event at the 2012 Summer Olympic Games was 21.89 meters. A shot must land within a sector with a central angle of 34.92^o. An official draws an arc across the landing area marking the farthest throw. How long is the arc?

about 13.3 meters

Trig Graphs

100

The horizontal length of each cycle of a graph is called the ______

Period

Bonus: What is the term used for one half the difference between the maximum and minimum value?

200

Draw the general shape of a sinusoidal (sine or cosine) graph

(Should look like a wave)

300

Identify the amplitude and period of g(x) = 3 cos (pix)

Amplitude = 3

Period = 2

Bonus: Describe the graph of g as a transformation of the graph of f(x) = cos x

400

Give two vertical asymptotes of the graph of g(x) = tan 2x

-Pi/4 and pi/4 (or any odd multiples of pi/4)

500

Describe the graph of g(x) = -3 sin 1/2(x - pi) as a transformation of its parent function.

Reflection in the x-axis; Vertical stretch by a factor of 3; Horizontal stretch by a factor of 2; Horizontal translation pi units right

Trig Identities

100

What trig function is a reciprocal of sine?

cosecant

200

True or False: cos(-x) = cos(x)

True

300

State the three Pythagorean identities

sin²x + cos²x = 1

1 + tan²x = sec²x

1 + cot²x = csc²x

400

Simplify sinx cosx secx

sinx

500

Verify the identity (sinx/cscx) + (cosx/secx) = 1

(Show work)

Solving Trig Expressions/Equations

100

Evaluate cos(pi/3). Give exact answer

1/2

Bonus: Evaluate csc(-pi/3)

200

cos(a - b) = ?

= cosa cosb + sina sinb

300

Find the exact value of sin(75^o)

(6^1/2 + 2^1/2)/4

400

Simplify tan(x - pi)

tan x

500

Solve cos(x + pi/4) + cos(x - pi/4) = 1 for x between 0 and pi

x = pi/4