Unit 6 Lesson 6 Trigonometric Ratios CCSS G-SRT 6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT 7: Explain and use the relationship between the sine and cosine of complementary angles. G-SRT 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Lesson Goals Understand the three basic trigonometric ratios are based on the side lengths of a right triangle. Write the three basic trigonometric ratios in fractional and decimal form. Use a chart or calculator to find the three basic trig ratios for a given angle. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

PREVIOUSLY IN MATH Ratios compare two quantities by division In a right triangle, the hypotenuse is the side opposite the right angle. The word “adjacent” means “next to” hypotenuse Room 12 is adjacent to Room 11

Definition Trigonometric Ratio A ratio formed by comparing the lengths of two sides of a right triangle from the “viewpoint” of a given acute angle.  Sine: leg length opposite an angle to the hypotenuse  Cosine: leg length adjacent an angle to the hypotenuse  Tangent: leg length opposite an angle to the leg length adjacent the angle

You Try B C A

B C A

Definition B C A

B C A

Trigonometric Ratio The Gabrielino–Tongva Indian Tribe that at one time lived in the area which we now know as Fullerton used the word SOHCAHTOA to help them remember the trigonometric ratios. S ine O pposite H ypotenuse C osine A djacent H ypotenuse T angent O pposite A djacent Bird Dancers Gabrielino/Tongva Indians of So Cal

Example B C A

Example B C A 1 1

You Try

Definition Trigonometric Identities An equation involving trig ratios that is true for all acute angles.  is the “x” for angles

Example A B C 4 3 5

Proof statementreason A B C a b c

Trigonometric Ratios Every acute angle has a sine, cosine, and tangent. These ratios are usually written as a four-digit decimal approximation. These ratios can be looked up in trigonometric tables or found with a scientific calculator.

Page 845 also the last page of your notes.

Example sin 34 o =

Example tan 65 o =

Example Using a scientific calculator.

Summary What is meant by the sine, cosine, and tangent of an angle?

p. 562: 10 – 20 e, 47, 48

Use a Trig Ratio Table or a calculator to find each value. Use your knowledge of a right triangle.