Trig. Functions & the Unit Circle

Trigonometry & the Unit CircleIf s a real number and P = (x,y) is apoint on the unit circle that corresponds to , then:

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VERY importantTrig. Identity

What is the Unit Circle?

•A circle with radius 1, centered at the origin (0,0)

•Used to find the trigonometric ratios of each of any angle that is a multiple of 30 or 45.

Filling out unit circle Activity!

•Create a 45-45-90 triangle with hypotenuse 1

•Create a 30-60-90 triangle with hypotenuse 1

•Label the lengths of each side•Use these triangles to find the x-y

coordinate of each angle’s point of intersection with the unit circle.

The 45-45-90 Triangle

1

The 30-60-90 Triangle

1

30

60

Signs of Trig. Functions on Unit Circle

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(− ,− )(+ ,− )

Where are the trig. functions positive?

AllSine

Tangent Cosine

All Students Take Calculus

Also true for Reciprocal Identities!!!

Example 1– Evaluate the Trig. Functions NO CALCULATOR

-1

0

DNE

0

√𝟑𝟐

𝟏𝟐

Example 2 – Find Trig. Functions Using a Point on the Unit Circle

•A point P(x,y) is shown on the unit circle. Find the values of the six trigonometric functions.

a. b.

Homework (Due Monday)

•Workbook p. 73: 21-26

•Study for Monday’s Unit Circle Quiz!!!