1. 4.4 Trigonometric Functions of any Angle Objective: Students will know how to evaluate trigonometric functions of any angle, and use reference angles to evaluate trigonometric functions.

2. Let θ be an angle in standard position, with (x, y) a point on the terminal side be a point distinct from the origin on the terminal side of θ. Let r =.

3. Ex 1) The point (-4, 10) is on the terminal side of an angle in standard position. Determine the exact values of the 6 trig functions. sin θ = csc θ = cos θ = sec θ = tan θ =cot θ =

4. Signs of Trig Functions

5. Ex 2) State the quadrant in which θ lies. a) tanθ >0 b) sec θ 0 and cos θ > 0. e) tan θ 0

6. Ex 3) Find the values of the 6 trig functions of θ Function ValueConstraint sin θ = 3/5θ is in QII sin θ = csc θ = cos θ = sec θ = tan θ =cot θ =

7. Ex 4) Find the values of the 6 trig functions of θ Function ValueConstraint tan θ = -15/8sin θ < 0 sin θ = csc θ = cos θ = sec θ = tan θ =cot θ =

8. reference angle: the acute angle formed by the terminal side of θ and the x-axis is called the reference angle

9. Ex 5) Find the reference angle θ’ for the special angle θ. Then sketch θ and θ’ in standard position. a)θ = 120º b) θ = -135º c) θ = -5 /6 d) θ = - /12

10. Ex 6) Evaluate the sine, cosine, and tangent without using a calculator. a)θ = -750º b)θ = -7 /6 sin θ = cos θ = tan θ = sin θ = cos θ = tan θ =

11. Ex 7) Find the indicated trig value in the specified quadrant. Function Quadrant Trig Value a) tan θ = 3/2IIIsec θ b) sin θ = 1/3IIcos θ

12. Example 8) Find two solutions of the equation in the first revolution. sin θ = ½ tan θ = -1 csc θ =