Section 9-1/9-2: Trigonometric Ratios April 16, 2012

Warm-up: (15 mins)

Sections 9-1/9-2 Trigonometric Ratios Objective: Today you will learn to find sine, cosine and tangent ratios for acute angles of right triangles. Trigger Fish: “Trig” Tang: “Tangent”

Investigation Right Triangles: sides and angles Draw right triangles with your assigned m ∠ A: Measure the sides (in cm) of each triangle and fill in this chart:

Investigation Right Triangles: sides and angles

Trigonometric Ratios: Sine

Trigonometric Ratios: Cosine

Trigonometric Ratios: Tangent

Trigonometric Ratios: Sine/Cosine/Tangent “SOH CAH TOA” Studying Our Homework Can Always Help To Obtain Achievement Some Of Her Children Are Having Trouble Over Algebra Some Old Hippy Caught Another Hippy Tripping On Acid Some Old Horse Caught Another Horse Taking Oats Away Saddle Our Horses Canter Away Happily to Other Adventures Some Old Helmets Can Allow Head Trauma On Accidents Make up your own!

Example 1: Find the following ratios for this triangle Leave in fraction form.

Example 2: Find sine, cosine, and tangent of angles A and B in each right triangle. Leave in fraction form.

Using your Calculator First ensure the calculators are set to use degrees for angles:

Using your Calculator

Example 3: Find missing side

Example 4: Find missing sides. Round to nearest tenth.

Inverse Functions To find the measure of angles given sides, use the inverse functions: sin -1 cos -1 tan -1

Example 5: Find m ∠ x to the nearest whole number

Example 6: Find missing angle measurements to the nearest whole number

Unit Circle Hypotenuse = 1, so Sin(angle) = y Cos(angle) = x Tan(angle) =

Wrap-up Today you learned to find sine, cosine and tangent ratios for acute angles of right triangles. Tomorrow you’ll learn to identify the angle of elevation and depression and use them with trigonometric ratios. Homework (H)  p. 472, # 1-16,  p. 479, # 1-17, Homework (R)  p. 472, # 1-16, 28  p. 479, # 1-17, 24