Unit Circle Review

Formulas

100

This trigonometry ratio uses the fraction adjacent over hypotenuse.

What is cosine(x)

200

This equation is a way of finding the x-coordinate on a unit circle.

What is x=cos(theta)

300

This trigonometry ratio uses the fraction opposite over hypotenuse.

What is sin(theta)

400

This equation gives us the y-coordinate on the unit circle.

What is y=sin(theta)

500

Given a Unit Circle, in order to calculate tan(theta), you divide what by what?

What is divide y by x?

Converting Radians/Degrees

100

The conversion from this radian measure to degrees is 180 degrees.

What is pi.

200

The conversion from this radian measure to degrees is 90 degrees.

What is pi/2.

300

The conversion from this radian measure to degrees is 225 degrees.

What is 5*pi/4.

400

The conversion from this radian measure to degrees is 330 degrees.

What is 11*pi/6.

500

The conversion from this radian measure to degrees is 390 degrees.

What is 13*pi/6.

Evaluating sin, cos and tan

100

Evaluate sin(90)

What is 1

200

Evaluate sin(150)

What is 1/2 or .5

300

Evaluate sin(4*pi/3).

What is - sqrt(3)/2

400

Evaluate sin(7*pi/4)

What is -sqrt(2)/2

500

Evaluate tan(pi/6)

sqrt(3) / 3

Evaluating sec, csc, and cot

100

Evaluate sec(45)

sqrt(2)

200

Evaluate sec(2*pi/3)

-2

300

Evaluate csc(2*pi/3)

2*sqrt(3)/3

400

Evaluate cot(3*pi/2)

0

500

Evaluate cot(pi)

Undefined

Applications

100

A 40 meter tall cliff overlooks a lake. A person is standing on the cliff and is looking at a boat in the lake. The angle of depression from the person to the boat is 45 degrees. Without using a calculator, determine how far the boat is from the base of the cliff.

What is 20*sqrt(2) meters?

200

A person is looking up to the top of a 20 foot tall tree with an angle of elevation of 30 degrees. Without using a calculator, what is the distance between the person and the top of the tree?

What is 40 feet?