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Trigonometry Review Problems Pre-Calculus Chapter 5 Draw the angle, and name its quadrant. Find a positive and negative co-terminal angle. Convert. 1. -465° 8 2. 3 -465° = ______ radians Quadrant:_____ Positive co-terminal angle:_____ ° = ______ rad. Negative co-terminal angle_____ ° = ____ rad. 8 = ____ ° 3 Quadrant:_____ Positive co-terminal angle:_____ ° = ______ rad. Negative co-terminal angle_____ ° = ____ rad. Find the reference angle for the given angle θ in standard position. 3. 295° 4. -490° 10 5. 3 θ′ = _________ θ′ = _________ θ′ = _________ 6. 5 8 θ′ = _________ Use the ordered pairs from the unit circle to find the exact value of each expression. 7. cos 150° 8. sin 225° 9. tan (-30°) 10. csc(90°) 11. sec(270°) 12. cot 45° 13. sin 3 14. cos 52 15. cot 116 16. sec( 73 ) 19. Determine each value to four decimal places. 8 b) sec( 130 ) 5 a) tan c) cot 5 3 17. csc(5 ) 18. tan 72 d) csc(340°) Find values for θ where… 20. 0° < θ < 360° to the nearest tenth of a degree 21. 0 < θ < 2π to the nearest hundredth of a radian sin θ = -0.3568 cot θ = 1.2479 θ = ___________________ θ = ___________________ In which quadrant does the terminal side of θ lie from standard position? 22. tan θ > 0 and csc θ < 0 23. sec θ < 0 and π < θ < 2π 24. cot 3 5 5 and sin 70 14 Given the following information, find the exact value of the six trig functions. 25. (5, 9) is a point on the terminal side of θ. 26. The terminal side of θ intersects the unit circle 2 5 5 . , at 5 5 sin θ = ______ cos θ = ______ tan θ = ______ sin θ = ______ cos θ = ______ tan θ = ______ csc θ = ______ sec θ = ______ cot θ = ______ 7 2 and cos θ > 0 (Draw the Δ.) 2 csc θ = ______ sec θ = ______ cot θ = ______ 19 28. 6 sin θ = ______ cos θ = ______ tan θ = ______ sin θ = ______ cos θ = ______ tan θ = ______ csc θ = ______ sec θ = ______ cot θ = ______ csc θ = ______ sec θ = ______ cot θ = ______ 27. csc Graph at least two cycles of the following functions. 30. g ( x) 3 csc( 2x) 29. f ( x) tan 14 x Period:_______ Domain:____________________________ Range: _____________________________ 31. h( x) 2 cot(3x ) Period:_______ Domain:____________________________ Range: _____________________________ 32. j ( x) cos( 12 x ) 3 Period:________ Phase Shift:_________ Domain:____________________________ Range: _____________________________ Period:____ Phase Shift:____ Vert. Trans:_____ Domain:____________________________ Range: _____________________________