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Chapter 1 Review Dual Credit Trigonometry – Meinke Name: ____________________________________ No Calculator Evaluate each expression. Rationalize if necessary. 1.) sin 300 2.) tan (−1350) 3.) sin(5 π /6) 4.) cos 330 0 5.) csc(2 π/3) 6.) tan (−2 π/3) 7.) sec(1800 ) 8.) cos (3 π/2) 9.) tan–1 ( − 12.) cos–1 3 ) 3 1 2 15.) cos(cos–1 ( 1 )) 3 10.) sin–1 ( − 2 ) 2 11.) sin–1 (–1) 13.) cos–1 ( − 1 ) 2 14.) tan–1 ( 16.) tan(tan–1 ( − 3 )) 3 1 ) 3 17.) cos(cos–1 2) Find the quadrants for which: 18.) cotx < 0 and cos > 0 19.) sinx < 0 and tanx > 0 20.) sec < 0 and csc > 0 21.) Complete the following table. Function Domain Range −1 f(x) = sin x −1 f(x) = cos x −1 f(x) = tan x 22.) Find the value of each of the 6 trigonometric function EXACTLY (simplified radicals) for θ = 5π/3. cos θ = ________ sec θ = _______ sin θ = ________ csc θ = _______ tan θ = ________ cot θ = _______ 23.) Given sec θ = 3 and sin θ <0 find the EXACT (simplified radicals) values of the remaining trigonometric functions. sin θ = _____________ csc θ = ____________ cos θ = ____________ sec θ = 3 tan θ = _____________ cot θ = _____________ Calculator Solve the following word problems. 24.) An 8-foot-long piece of 2-by-4 wood is used to prop up a fence. If the 2-by-4 makes a 40° angle with the ground, how high above the ground is the point where the 2-by-4 contacts the fence? 25.) John views the top of a 458 foot water tower at an angle of elevation of 51º. How far away from the tower is John standing? 26.) A person is standing 10 feet away from a 37 ft tree. What is the angle of elevation from the person to the top of the tree? Express your answer in degrees. 27.) A bicycle wheel is rotating at a rate of 2 radians per second. There is a speck of dirt stuck to the middle of one of the spokes, and another speck of dirt stuck to the wheel’s rim, located 8 inches from the center. Tell which speck has a faster angular speed, and which speck has a faster linear speed. Explain and compute the angular and linear speeds of both specks of dirt. 28.) Convert 250º to radians. Leave the answer in terms of π . 29.) Find the degree measure of 11π 9 .