Exam 1: Trigonometry

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When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​ Y = 0.001 sin 880πt, ​ Where t is the time (in seconds). ​ What is the period of the function? ​

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Use the value of the trigonometric function to find Use the value of the trigonometric function to find   . ​   ​ . ​ Use the value of the trigonometric function to find   . ​   ​ ​

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The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. ​ The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. ​   ​ ​

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Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode.) ​ Tan 306° ​

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Find a model for simple harmonic motion satisfying the specified conditions. ​ Displacement (t = 0): 0 Amplitude: 5 centimeters Period: 2 seconds ​

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An electric hoist is being used to lift a beam.The diameter of the drum on the hoist is 16 inches, and the beam must be raised 2 feet.Find the number of degrees through which the drum must rotate.Round your answer to nearest whole number. ​ An electric hoist is being used to lift a beam.The diameter of the drum on the hoist is 16 inches, and the beam must be raised 2 feet.Find the number of degrees through which the drum must rotate.Round your answer to nearest whole number. ​   ​a = 16, b = 2 ​ ​a = 16, b = 2 ​

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Select the graph of the function below.Include two full periods. ​ Select the graph of the function below.Include two full periods. ​   ​ ​

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Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window. ​ Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window. ​   ​ ​

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Find the exact value of csc θ, using the triangle shown in the figure below, if a = 3 and b = 4. Find the exact value of csc θ, using the triangle shown in the figure below, if a = 3 and b = 4.

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Convert the angle measure from degrees to radians.Round to three decimal places. ​ -0)51° ​

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Find an algebraic expression that is equivalent to the expression.. ​ Find an algebraic expression that is equivalent to the expression.. ​   ​ ​

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Determine the quadrant in which an angle, θ, lies if θ = 5.00 radians.

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An observer in a lighthouse a = 340 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4º and 6.5º (see figure).How far apart are the ships? Round your answer to one decimal place. ​ An observer in a lighthouse a = 340 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 4º and 6.5º (see figure).How far apart are the ships? Round your answer to one decimal place. ​   ​ ​

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Determine the exact values of the three trigonometric functions csc, sec, and cot of the angle θ. ​ Determine the exact values of the three trigonometric functions csc, sec, and cot of the angle θ. ​   ​ Where a = 15 and b = 8. ​ ​ Where a = 15 and b = 8. ​

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Select the graph of the function below.Include two full periods. ​ Select the graph of the function below.Include two full periods. ​   ​ ​

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Use the value of the trigonometric function to find Use the value of the trigonometric function to find   . ​   ​ . ​ Use the value of the trigonometric function to find   . ​   ​ ​

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Consider the function given by ​ Consider the function given by ​   ​ Use a graphing utility to select the graph of the function. ​ ​ Use a graphing utility to select the graph of the function. ​

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Find the period and amplitude. ​ Find the period and amplitude. ​   ​ ​

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For the simple harmonic motion described by the trigonometric function, find the frequency per second. ​ For the simple harmonic motion described by the trigonometric function, find the frequency per second. ​   ​ ​

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Evaluate the trigonometric function using its period as an aid. ​ Evaluate the trigonometric function using its period as an aid. ​   ​ ​

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