trigonometry trigonometric ratio sine cosine tangent inverse sine

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trigonometry trigonometric ratio sine cosine tangent inverse sine

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Presentation transcript:

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

Mathematical Practices Content Standards 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. Mathematical Practices 4 Model with mathematics. 1 Make sense of problems and persevere in solving them. Vocabulary

Concept

Find Sine, Cosine, and Tangent Ratios A. Express sin L, cos L, and tan L as a fraction & as a decimal to the nearest hundredth. B. Express sin N, cos N, tan N as a fraction & as a decimal to the nearest hundredth. Example 1

A. Express sin A, cos A, and tan A as a fraction & as a decimal to the nearest hundredth. B. Express sin B, cos B, and tan B as a fraction & as a decimal to the nearest hundredth. Example 1

Estimate Measures Using Trigonometry 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? Example 3

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°, about how high does the ramp rise off the ground to the nearest inch? Example 3

Concept

A. Use a calculator to find the measure of P to the nearest tenth. Find Angle Measures Using Inverse Trigonometric Ratios A. Use a calculator to find the measure of P to the nearest tenth. B. Use a calculator to find the measure of D to the nearest tenth. Example 4

Solve a Right Triangle Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree. Example 5

Solve the right triangle Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. A. mA = 36°, mB = 54°, AB = 13.6 B. mA = 54°, mB = 36°, AB = 13.6 C. mA = 36°, mB = 54°, AB = 16.3 D. mA = 54°, mB = 36°, AB = 16.3 Example 5