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

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

The six trigonometric functions: adjacent opposite hypotenuse θ

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

Trigonometric Identities: You should already have these

These are the: Co-function Identities

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

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

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

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

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? θ

angle value of the angle angle value of the angle

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.

Go! Do!