1. Created by Judy L. McDaniel

2. Ratios of the side lengths of a triangle are called. You can use,, and ratios to find the measures of sides or angles of right triangles that may be missing. Right Trigonometric Ratios SineCosineTangent

3. NAMEWRITTEN DEFINITION sine of ∠A sin A or cosine of ∠A cos A or tangent of ∠A tan A or A

4. To calculate a trigonometric ratio, the lengths of the appropriate sides in the correct. Make sure your calculators are in mode when finding trigonometric ratios. The and of any acute angle of a right triangle is always. The of any acute angle of a right triangle is sometimes and sometimes. Substitute Ratio DEGREES Sine Cosine LessThan 1 WHY? The Hypotenuse which is in the Denominator is ALWAYS longer than either of the legs in the Numerator GreaterThan 1 Tangent LessThan

5. Problem 1 Finding Trigonometric Ratios Find sin, cos and tan for the angles shown. A.A B. A B C B C sin A sin C cos A cos C tan A tan C 15 20 2525 9 12 15 Angle A (h)(h) (a)(a) (o)(o) Angle C (h)(h) (o)(o) (a)(a)

6. Problem 2 Finding Trigonometric Ratios(Calculator) What is the value of each expression? A.sin 80°B.sin 45° C.cos 9°D.cos 45° E.tan 45°F.sin 15° Describe the relationship between sin 45° and cos 45°. Round to the nearest ten-thousandths (4 dec.) 0.98480.7071 0.9877 0.7071 10.2588 They are equal Because a 45-45-90 triangle, is isosceles, the legs are the same length. This creates the same ratios (fractions) for sine and cosine.