1 / 18

4.3 Right Triangle Trigonometry

4.3 Right Triangle Trigonometry. Objectives: Evaluate trigonometric functions of acute angles Use the fundamental trigonometric identities Use trigonometric functions to model and solve real-life problems. Trigonometric Functions. Given a right triangle with acute angle . hyp. opp. .

holmes-hull
Download Presentation

4.3 Right Triangle Trigonometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4.3 Right Triangle Trigonometry Objectives: Evaluate trigonometric functions of acute angles Use the fundamental trigonometric identities Use trigonometric functions to model and solve real-life problems

  2. Trigonometric Functions Given a right triangle with acute angle  hyp opp  adj 4.3 Right Triangle Trigonometry

  3. Evaluate the six trig functions of the angle  shown in the right triangle sin  = cos  = tan  = csc  = sec  = cot  =  5 13 12 Example 1 4.3 Right Triangle Trigonometry

  4. 30° 15 x Example 2 • Find the value of x for the right triangle shown 4.3 Right Triangle Trigonometry

  5. B 62° c 6 A C b Example 3 • Solve ∆ABC 4.3 Right Triangle Trigonometry

  6. B c a 30° A C You Try • Solve ∆ABC 4.3 Right Triangle Trigonometry

  7. Special Triangles30º-60°-90° Recall the conversions 30°= 60°= 60° 2 1 30° 4.3 Right Triangle Trigonometry

  8. Special Triangles45º-45°-90° • Recall the conversion • 45°= 45° 1 45° 1 4.3 Right Triangle Trigonometry

  9. Co-functions of Complementary Angles • Look back at the sines and cosines for the 30-60-90 triangle • Note that sin 30°=cos 60° • Co-functions of complementary angles are equivalent 4.3 Right Triangle Trigonometry

  10. Trigonometric Identities • Reciprocal Identities 4.3 Right Triangle Trigonometry

  11. Trigonometric Identities • Quotient Identities 4.3 Right Triangle Trigonometry

  12. Trigonometric Identities • Pythagorean Identities Note: sin2 is (sin )2 not sin (2) 4.3 Right Triangle Trigonometry

  13. Example 4 • Given sin=0.6, find the value of cos • Given sin=0.6, find the value of tan 4.3 Right Triangle Trigonometry

  14. Example 5 Use trigonometric identities to transform one side of the equation into the other. • cossec=1 • (sec+tan)(sec-tan)=1 4.3 Right Triangle Trigonometry

  15. Surveying • A surveyor is standing 50 ft from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? 4.3 Right Triangle Trigonometry

  16. River Walk • You are 200 yards from a river. Rather than walking directly to the river, you walk 400 yards along a straight path to the river’s edge. Find the acute angle ө between this path and the river’s edge. 4.3 Right Triangle Trigonometry

  17. Skateboarding • Find the length c of the skateboard ramp. 4.3 Right Triangle Trigonometry

  18. Homework • Star Wars Worksheet • Page 285 44-54 even, 79-82 all 4.3 Right Triangle Trigonometry

More Related