# Tan θ cot θ sec θ csc θ 8 6 pts if the point 2 5

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trigonometric functions. tan( θ ) = cot( θ ) = sec( θ ) = csc( θ ) = 8. (6 pts.) If the point (-2,-5) is on the terminal side of an angle θ , obtain the exact value of each of the six trigonometric functions of θ . sin( θ ) = cos( θ ) = tan( θ ) = cot( θ ) = sec( θ ) = csc( θ ) = 9. (4 pts.) In which quadrant is sin θ < 0 and cot θ > 0 ? 10. (4 pts.) What is the reference angle θ r for an angle θ = -135°? θ r = 11. (4 pts.) What is the exact value of tan(19 π /6) ? tan(19 π /6) = 12. (4 pts.) If cos θ = .4, find cos( θ + π ). cos( θ + π ) =

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TEST-01/MAC1114 Page 3 of 4 13. (5 pts.) Suppose cos θ = -(1/4) and tan θ > 0. What is the exact value of each of the remaining trigonometric functions? sec( θ ) = tan( θ ) = sin( θ ) = csc( θ ) = cot( θ ) = 14. (5 pts.) Suppose a is a number such that if f(x) = csc(x), then f(a) = -5. Obtain the exact value of the following: f(-a) = f(a) + f(a + 4 π ) + f(a + 16 π ) = 15. ( pts.) Fill in the following table with the information requested concerning domain, range, and period. Function Name Domain (in radians) Range Period (in radians) sin( θ ) cos( θ ) tan( θ ) cot( θ ) sec( θ ) csc( θ ) 16. (2 pts.) Use a calculator to obtain the approximate value of each of the following expressions. Round your answer to two decimal places. sin 1 sin 1°
TEST-01/MAC1114 Page 4 of 4 17. (5 pts.) Carefully sketch y = sin(x) through two periods that are symmetric about the origin. Use radian measure and label carefully. y x 18. (5 pts.) Carefully sketch y = cos(x) through two periods that are symmetric about the origin. Use radian measure and label carefully. y x 19. (5 pts.) Carefully sketch y = tan(x) through one period. Use radian measure and label carefully. y x 20. (5 pts.) Carefully sketch y = csc(x) through one period. Use radian measure and label carefully. y x
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