sample3exam3 (Math 121)

# sample3exam3 (Math 121) - 1 6(12 pts The graph of a...

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Math 121 Precalculus NAME: Hour Exam Three TA: November 14, 2003 Give complete explanations, not just answers, for full credit. Give exact answers whenever possible, otherwise give answers accurate to two decimal places. Sketch any calculator graph you use including the axes with a scale. 1. (16 pts) Give the exact value of the following trigonometrical expressions: (a) cos( π 3 ) (b) sec( - π 4 ) (c) tan - 1 (1) (d) sec( - 7 π ) (e) sin - 1 ( 3 2 ). 2. (12 pts) If cos( t ) = 2 3 and - π 2 < t < π 2 , Fnd tan( t ). 3. (12 pts) Which of the following statements are true for all values of x ? Which are false? Brie±y explain your reason for each TRUE or ²ALSE answer. (a) sin 2 ( x ) + cos 2 ( x ) = 1 (b) sin( x ) cos( - x ) = tan( x ) (c) sin( π + x ) = - sin( x ) (d) sin( π 2 + x ) = cos x 4. (12 pts) ²ind an algebraic expression in v for the expression tan(sin - 1 v ). 5. (12 pts) Use your knowledge of special values to Fnd all of the solutions of the equation cos(2 x ) = 1 2 . (Give exact answers for full credit.) There are more questions on the reverse side.

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Unformatted text preview: 1 6. (12 pts) The graph of a function that describes a simple harmonic motion is shown below. (a) What is the amplitude of the function? (b) What is the period of the function? (c) What is a possible formula for the function? f ( t ) t 2-2 p 2 7. (12 pts) The function h ( t ) models the height in feet at time t seconds of a rider on a Ferris wheel. h ( t ) =-16 cos( πt 40 ) + 24 (a) What is the maximum height the rider reaches? (b) How long does it take for one revolution of the wheel? (c) How high is the rider when t=50 seconds? (d) When is the ±rst time, after t = 0, the rider reaches a height of 24 feet? 8. (12 pts) A riding lawnmower has wheels that are 12 inches in diameter. If the lawn-mower is traveling 3 miles per hour, what is the angular speed of the wheels in radians per second? (1 mile = 5280 feet; 1 foot = 12 inches ) 2...
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sample3exam3 (Math 121) - 1 6(12 pts The graph of a...

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