1. SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 4.3 Right Triangle Trigonometry

2. Homework for section 4.3 p306 # 7-35 eoo, 37-45, 49, 51, 57- 61, 67, 70, 72

3. The six trigonometric functions: adjacent opposite hypotenuse θ

4. Find the trigonometric functions for the following: θ 3 4 hypotenuse Use the Pythagorean Theorem to find the hypotenuse. 5

5. Trigonometric Identities: You should already have these

6. These are the: Co-function Identities

7. Trigonometric Identities Pythagorean Identities (This is also the formula for a circle…) a b c x y r x y r

8. Two more identities can be derived from this identity. sin 2 θ cos 2 θ csc 2 θ cot 2 θ sin 2 θ 1 + = 1 tan 2 θ sin 2 θ cos 2 θ sec 2 θ 1 cos 2 θ + = 1

9. Example : Let θ be an acute angle such that sin θ = 0.6 Find the values of a) cos θ b) tan θ θ 0.6 1 0.8

10. Example : A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5 ◦. How tall is the tree? 50 ft 71.5 ◦ y

11. Example : You are on a patch of grass 300 feet distant from a lake. You decide to walk in a straight line at an angle towards the lake. The distance you travel is 500 feet. What is the angle made between your path and the edge of the lake? 300 500 θ

12. angle value of the angle angle value of the angle

13. Given the angle; Find the value of the trig function of that angle. Given the value of the trig function of an angle; Find the angle.

14. Go! Do!