Warm-Up: February 3/4, 2016 Consider θ =60˚ Convert θ into radians Find the complement of θ, expressed in both degrees and radians Find the supplement of θ, expressed in both degrees and radians Find two angles that are coterminal to θ, expressed in both degrees and radians

Warm-Up: February 3/4, 2016 Consider θ =60˚ Convert θ into radians complement of θ: supplement of θ: two angles coterminal to θ:

Homework Questions

Making Waves Activity You have 45 minutes for the “Making Waves” activity. Work in your assigned seat. Work with your partner, but each of you must complete your own.

Trigonometric Functions: The Unit Circle Section 4.2

Unit Circle A unit circle is a circle with radius = 1 The center of a unit circle is at the origin of a rectangular coordinate system (x-y plane) The equation of a unit circle is The point on the unit circle at angle θ corresponds to sine and cosine of θ

All Students Take Calculus

The Six Trigonometric Functions Name Abbreviation Relation to (x, y) Restriction Sine sin y/1=y Cosine cos x/1=x Tangent tan y/x x≠0 Cosecant csc 1/y y≠0 Secant sec 1/x Cotangent cot x/y

Warm-Up: February 5, 2016 Consider θ =135˚ Convert θ into radians Find the complement of θ, expressed in both degrees and radians Find the supplement of θ, expressed in both degrees and radians Find two angles that are coterminal to θ, expressed in both degrees and radians

Warm-Up: February 5, 2016 Consider θ =135˚ Convert θ into radians complement of θ: supplement of θ: two angles coterminal to θ:

Homework Questions?

Trig Function Relationships

Example 1 Determine the value of the six trigonometric functions of 240˚. You may not use a calculator.

You-Try #1 Determine the value of the six trigonometric functions of 135˚. You may not use a calculator.

You-Try #2 Determine the value of the six trigonometric functions of π. You may not use a calculator.

Even and Odd Cosine and Secant are even. cos −𝜃 = cos 𝜃 sec −𝜃 = sec 𝜃 Sine, Cosecant, Tangent, and Cotangent are odd. sin −𝜃 =− sin 𝜃 csc −𝜃 =− csc 𝜃 tan −𝜃 =− tan 𝜃 cot −𝜃 =− cot 𝜃

You-Try #4 Show two different ways to find sin − 𝜋 3 with the unit circle. You may not use a calculator.

Pythagorean Identities Using and we can get the following identities.

Example 6 Given that and find the value of the rest of the trigonometric functions

You-Try #6 Given that and find the value of the rest of the trigonometric functions

Cofunctions (Section 4.3) The value of a trig function of an angle is equal to the value of the cofunction of the complement of the angle If 𝜃 is in radians, replace 90˚ with

Example 4 (Section 4.3) Find a cofunction with the same value as the given function.

You-Try #4 (Section 4.3) Find a cofunction with the same value as the given function.

Trig Functions Values Table

Assignments Read Section 4.2 Page 450 #1-25 Every Other Odd, #27-45 Odd Page 462 #21-27 odd No calculators!