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# 15 Trigonometry Problems : Angular Velocity, Shadows, Waves and Triangles

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Trigonometry Review
1. Assume the angle of inclination of the sun is given by Theta = (pi/12)t, where t is the number of hours after sunrise. Suppose we have a 10 meter high flagpole.
a. What is the angular velocity of the sun?
b. Write an equation for the length of the flagpole's shadow when the angle of the sun is theta radians.
c. Write an equation for the length of the flagpole's shadow t hours after sunrise.
d. If the sun rises at 6 am. when will the flagpole's shadow be 10 meters long?
e. If you stand at the tip of the shadow, how far will you be from the top of the flagpole?

2. The height of a wave is given by the function h(t) = 4 cos(wt), where t is in seconds. Suppose the height of the wave is 3 feet at 10 seconds.
a. What is the height of the wave at 20 seconds?
b. What is the height of the wave at 40 seconds?
c. What is the height of the wave at 5 seconds?

3. Consider triangle ABC. Suppose angle A is 45, the side opposite B is 3 meters, and the side opposite A is 2 meters. Find all the other sides and angles.

4. Write a function to model the day to day temperature of Metropolis. Suppose that the low temperature of 62° F is at 2 a.m. an(l the high temperature of 82 is at 2 p.m.
a. What is the period of your function?
b. What is the amplitude of your function?
c. What is the temperature at 6 a.m.. 8 a.m., and 10 p.m.

5. Suppose that you kick a ball into the air with a velocity of 20 meters per second at an angle of 30. If the ball stays airborne for 2 seconds and loses no horizontal velocity. how far (loc it go?

6. Suppose that you are bug stuck in the treads of a bicycle tire. If the tire has a radius of 13 inches and the tires are spinning at 180 revolutions per minute. Write a parametric equation for your position after t seconds.

7. Using parametric equations and simple trigonometric identity, find the angle that will maximize the horizontal distance of a projectile launched from the ground.