Trig – Section 2 The Unit Circle

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Presentation transcript:

Trig – Section 2 The Unit Circle Essential Questions: What are the values for special right triangles? How do you generate the unit circle? Define the six trig ratios in terms of x and y.

45-45-90 Right Triangles In a 45-45-90 right triangle, the hypotenuse is times as long as the leg. 45 1

Ex.1 Find the missing sides. 45 6 45 3 c) a) b) 45

30-60-90 Right Triangle In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg. 30 60 1 2

Ex 2. Find the missing sides. 30 4 a) b) 60 c) 60 18

Class Work Special Right Triangles Wkst

The Unit Circle A circle where the radius equals 1. On your special triangles worksheet, convert all of the radii to unit 1 and find the new length of each side. Discuss what you notice about 30, 45, 60 with your shoulder partner.

Constructing Sine: Cosine: Tangent:

Constructing Sine, Cosine, Tangent:

Constructing Sine, Cosine, Tangent:

What is the coordinate for this point? y x

Pass out Unit Circle worksheet Fill in degrees only for each circle on back Go over answers Pass out Hand made Circle worksheet and find point of each circle That is bold. Transfer information onto large unit circle Stop for today!

What is the circumference Of a circle with a radius of 1?

These are called Radians:

Radians A radian is another form of measuring angles. The radian measure of an angle drawn in standard position in the plane is equal to the length of the arc on the unit circle subtended by that angle. Radian Measure

What would be the degrees of these radian measures?

What will be the radian measure of these arcs?

What will be the degree measure of these?

Relationship between Degrees and Radians To convert degrees to radians, multiply by To convert radians to degrees, multiply by

Ex 3. Find the degrees or radians of each:

What is the coordinate for this point?

Label all the coordinates.

What are the coordinates of ?

What are the coordinates of ?

Fill in the Unit Circle

HW #2 Unit Circle Worksheet