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7.4 Trigonometry Notes Name:_________________________________ What is Trigonometry? What is a trigonometric ratio? The three most common trigonometric ratios are: Trig Definitions: SOH CAH TOA Some ways to Remember SOH CAH TOA Some Old Hillbilly Caught Another Hillbilly Throwing Old Apples She Offered Her Cat A Heaping Teaspoon of Acid. Key Concepts of Trigonometric Ratios What’s Constant? What Changes? Steps to Solve Trig Problems: Step 1: Draw a triangle to fit problem Step 2: Label sides from angle’s view - H: hypotenuse - O: opposite - A: adjacent Step 3: Identify trig function to use - Circle what values you have or are looking for - SOH CAH TOA Step 4: Set up an equation. Step 5: Solve for variable Example 1: Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal rounded to nearest hundredth. Example 2: Find x. Example 3: Find x. Check Yourself: Find x. What trig function should you use? a. b. c. Example 4: EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Step 1: Draw a triangle to fit problem Step 2: Label sides from angle’s view Step 3: Identify trig function to use Step 4: Set up equation Step 5: Solve for variable Example 5: CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, how high does the ramp rise off the ground to the nearest inch? How to Find an Angle: In trigonometry, you can find the measure of the angle by using the inverse of sine, cosine, and tangent. Example 6: Find x. Trig Practice 1) Labels the sides (Opposite – Hypotenuse – Adjacent) from the angle’s point of view 2) Based on the two sides, and the labels you gave them, choose the sine, cosine or tangent ratio (SOH – CAH – TOA) 3) Set up the equation base on which trig ratio you chose in step 2: sin( ) O A O , cos( ) , tan( ) H H A