1 1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. – 3 2 E x ami n a t i o n Trigonometric Functions Clearly number your answers and save them in a Word file. Upload your file as instructed in the Lesson 2 Review. Go to http://www.takeexamsonline.com to submit your answers online. Click on Take Exam next to Lesson 4. Then click on Submit Files. Questions 1–20: Answer the following questions. EXAMINATION NUMBER 00769700 2 Examination 4. Prove that tan2 – 1 + cos2 = tan2 sin2 . 5. Prove that tan sin + cos = sec . 6. Prove that = cos + sin . 7. Prove that . 8. Prove that = cos – cot cos . 9. Find a counterexample to shows that the equation sec – cos = sin sec is not an identity. sin cos tan sin cos tan 2 2 ? ? ? ? ? ? -+ 1+ tan 1 tan sec +2tan 1 tan 2 2 ?? ? ? – – ? = tan cos +sin sin2 2 ? ? ? ? Examination 3 10. Write tan as a function of only. 11. Write cos as a function of only. 12. Write cos(–83°) as a function of a positive angle. 13. Write sin(125°) in terms of its cofunction. Make sure your answer is a function of a positive angle. 14. Find the exact value of sin(195°). 15. Sketch a graph of y = sin(–2x), paying particular attention to the critical points. ? p + 3 ?? ????? ???? p ß 4 – ?? ????? ???? 24 –4 –2 p 2p 4 Examination 16. If cot 2= with 0 2, find cos, sin, and tan. 17. Find the exact value of sin2if cos= (in Quadrant I). 18. Find the exact value of tan2if sin= (in Quadrant II). 19. Solve sin 2x + sin x = 0 for 0 x 2. 20. Write 2sin37°sin26° as a sum (or difference). 5 12 455 13

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