Splash Screen. Then/Now You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles.

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Presentation transcript:

Splash Screen

Then/Now You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle measures in right triangles.

Vocabulary trigonometry trigonometric ratio sine cosine tangent inverse sine inverse cosine inverse tangent

Concept

Example 1 Find Sine, Cosine, and Tangent Ratios A. Express sin L as a fraction and as a decimal to the nearest hundredth. Answer:

Example 1 Find Sine, Cosine, and Tangent Ratios B. Express cos L as a fraction and as a decimal to the nearest hundredth. Answer:

Example 1 Find Sine, Cosine, and Tangent Ratios C. Express tan L as a fraction and as a decimal to the nearest hundredth. Answer:

Example 1 Find Sine, Cosine, and Tangent Ratios D. Express sin N as a fraction and as a decimal to the nearest hundredth. Answer:

Example 1 Find Sine, Cosine, and Tangent Ratios E. Express cos N as a fraction and as a decimal to the nearest hundredth. Answer:

Example 1 Find Sine, Cosine, and Tangent Ratios F. Express tan N as a fraction and as a decimal to the nearest hundredth. Answer:

Example 1 A. Find sin A. A. B. C. D.

Example 1 B. Find cos A. A. B. C. D.

Example 1 C. Find tan A. A. B. C. D.

Example 1 D. Find sin B. A. B. C. D.

Example 1 E. Find cos B. A. B. C. D.

Example 1 F. Find tan B. A. B. C. D.

Example 2 Use Special Right Triangles to Find Trigonometric Ratios Use a special right triangle to express the cosine of 60° as a fraction and as a decimal to the nearest hundredth. Draw and label the side lengths of a 30°-60°-90° right triangle, with x as the length of the shorter leg and 2x as the length of the hypotenuse. The side adjacent to the 60° angle has a measure of x.

Example 2 Use Special Right Triangles to Find Trigonometric Ratios Definition of cosine ratio Substitution Simplify.

Example 2 Use a special right triangle to express the tangent of 60° as a fraction and as a decimal to the nearest hundredth. A. B. C. D.

Homework: Pg. 573 #’s 1 - 7