1. Pg. 324 Homework Memorize familiar radian measure angles Pg. 323#2 – 52 even Pg. 361#1 – 13 all

2. 6.5 Trig Functions of an Acute Angle Trig Functions The six trig functions of any angle 0° < Ɵ < 90° are defined as follows: Also, we know that from the basic three trig functions:

3. 6.5 Trig Functions of an Acute Angle Triangle Trig We use right triangles because they allow us to use the Pythagorean Theorem, which makes solving a much easier process! Because 30°, 45° and 60° occur frequently, we will learn and memorize those triangles!! If c = 2, determine the lengths of a and b and find the six trig values at 30° and 60°.

4. 6.5 Trig Functions of an Acute Angle More Trig Triangles If a = 1, determine the length of c and find the six trig values. Cofunctions of Complementary Angles If Ɵ is any acute trig angle, a trig function value of Ɵ is equal to the cofunction of the complement of Ɵ, as follows:

5. 6.5 Trig Functions of an Acute Angle Example: Show that are cofunctions. Let Ɵ be an acute angle such that sin Ɵ = ¾. Find all the trig functions of Ɵ. One angle of a right triangle measures 42°, and the hypotenuse has length of 10. Find the measures of the remaining sides.

6. 6.5 Trig Functions of an Acute Angle Example: They hypotenuse and one leg of a triangle measure 8 and 5 respectively. Find the measure of angle Ɵ formed by these two sides. Trig Functions of Any Angle Let Ɵ be an angle in standard position, P(x, y) a point other than the origin on the terminal side of P, and r = The six trig values of Ɵ are defined as follows:

7. 6.5 Trig Functions of an Acute Angle Example: Find the values of the six trig functions at an angle Ɵ in standard form with point P(2, 4) on its terminal side. **Note** If an angle does not appear acute in the first quadrant, you can work in any of the four quadrants to make the angle acute!! Find the values of all six trig functions and the angle of measure of angle Ɵ, where P(-3, 2) is a point on the terminal side of Ɵ. Find all the values of all six trig functions for the quadrantal angles of: