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Test One – Trigonometry – Fall 2004
Name _______________________________________
This page must be done without the use of the graphing calculator. All fraction answers must be reduced
and all radical answers must be simplified.
(4 points each question)
Evaluate each of the following.
____________1a. sin 60º
____________1b. sin 300º
____________2a. sec 30º
____________2b. sec 330º
____________3a. tan 45º
____________3b. tan 135º
____________4a. cos 90º
____________4b. tan 270º
____________5a. cot 180º
____________5b. cos 0º
____________6a. Evaluate cos 90º + sin 60º
____________6b. Evaluate 5 sin2 45º
____________7. Evaluate cos2 57º + sin2 57º
8. Label each of the following as P (possible) or NP (not possible)
____________8a. sin θ = 0.2356
____________8b sec θ = -8.2356
9. Give the SIGN (+ or -) for each of the following:
____________9a. sin 312º
____________9b. csc 104º
____________10. If sin θ = 1/2, determine θ in the interval [0, 360º)
Test one – Trigonometry – Fall 2004
Name __________________________________________
YOU MAY USE YOUR CALCULATOR ON THIS PORTION OF THE EXAM. HOWEVER EXACT
ANSWER ARE REQUIRED. ROUNDED DECIMALS WILL NOT BE ACCEPTED.*****
____________11. Determine the tangent of an angle in standard position whose terminal side
passes through (5, 17)
____________12. Determine the sine of an angle in standard position whose terminal side passes
through (-3, 4)
____________13. Determine the cosine of an angle in standard position whose terminal side passes
through (-5, 2)
____________ 14. If sec θ = 3 and θ is in quadrant four, determine cos θ.
____________ 15. If sin θ = 4/7 and θ is in quadrant two, determine sec θ.
____________ 16. Give the complement of 57º 34' 17". Give your answer in degrees, minutes and seconds.
17 – 20. Determine the value of x in each of the diagrams.
____________17.
____________18.
4x - 47
5x
2x+7
2x + 20
6x + 40
____________ 19.
____________ 20.
16
x
30º
7
x
11
14
YOUR ANSWERS ON THE REMAINDER OF THE EXAM MAY BE IN DECIMAL FORM,
ROUNDED TO THE NEAREST THOUSANDTH.
____________ 21. Convert 75.8972º to degrees, minutes and seconds.
You may round your answer to the nearest second.
____________ 22. Find the smallest positive angle coterminal with -258º
____________ 23. Determine cos (152.72º)
____________ 24. Determine sec (152.72º)
____________ 25. If tan θ = 16.8712, determine θ in quadrant one.
____________ 26. If cot θ = 16.8712, determine θ in quadrant one.
____________ 27. Given the formula F = w sin θ, determine the grade resistance of a 2800lb
car traveling on a downhill grade of -1.26º
____________ 28. Given a right triangle with A = 57º 23' and a = 34.78 inches, determine the value of b.
____________ 29. The shadow of a vertical tower is 72.87 m long when the angle
of elevation of the sun is 31.5º.
Find the height of the tower.
31.5o
____________ 30. Evaluate
sin 2523'14"
cos 2523'14"
__________________BONUS: Sketch a 147º angle is standard position. Place a point 3 spaces out on the
terminal side (so that the distance from the origin to the point is 3). Give the coordinates of
the point to the nearest thousandth.