mac1147_unit3_review_2_b

mac1147_unit3_review_2_b - Review – Unit III Name one...

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Unformatted text preview: Review – Unit III Name one positive and one negative angle coterminal 2π with . 3 Give the general formula for all angles coterminal with 2π . 3 2π Find the reference angle α for θ = . 3 Find: sin 2π 3 cos Suppose that a machine contains a wheel of diameter 3ft. rotating at 10 revolutions per second. Find the linear speed of the wheel in feet per min. 4 Given: cos t = − , 7 Find: cot t csc t > 0 . 2π 3 cos ( 90° − t ) I II π⎞ ⎛ Given the function: y = 1 + 2sin ⎜ 3 x + ⎟ . 2⎠ ⎝ Find the amplitude, period, and phase shift. Evaluate: cot 270° + 4sin180° ⎛ π⎞ tan π − 4sin ⎜ − ⎟ + 5cos 2 π ⎝ 2⎠ cos 31π 4 ⎛ 11π ⎞ cot ⎜ ⎟ ⎝2⎠ ⎛ 13π ⎞ csc ⎜ − ⎟ ⎝ 3⎠ III IV π⎞ ⎛ Find all asymptotes of the graph of y = cot ⎜ 2 x − ⎟ . 3⎠ ⎝ Given: tan u = − Find: Simplify: 1 + tan 2 θ = 1 + cot 2 θ sin 2u cos u 2 tan V 3π 3 and < u < 2π 4 2 u 2 VI Find sin 75° using the half-angle formula. Evaluate without a calculator: sin −1 ( −1) ⎛ 2⎞ cos −1 ⎜ − ⎟ ⎝ 2⎠ sin ( cos −1 ( −1) ) ⎛ 10π ⎞ cos −1 ⎜ cos ⎟ 3⎠ ⎝ VII VIII ⎛ 9π ⎞ sin −1 ⎜ sin ⎟ 8⎠ ⎝ (a) Solve the equation on the interval [0,2π ) . (b) Find all solutions of the equation. cos 2θ − cosθ = −1 ⎛ ⎛ 1 ⎞⎞ Evaluate: tan ⎜ cos −1 ⎜ − ⎟ ⎟ ⎝ 5⎠⎠ ⎝ IX X A tunnel for a new highway is to be cut through a mountain that is 260 feet high. At a distance 200 feet from the base of the mountain the angle of elevation is 36 ° . From a distance of 150 feet on the other side, the angle of elevation is 47 ° . Approximate the length of the tunnel to the nearest foot. XI ...
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mac1147_unit3_review_2_b - Review – Unit III Name one...

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