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Reworked Part (Exam2)

# Reworked Part (Exam2) - x sin x)tan x to one trigonometric...

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Math 1613, Fall 2011 Reworked Part of Exam 2 Due Date: 11/2/2011 Name (Print): —————————————————————– Note: You must show your work very carefully to receive credit. Staple this exam when you turn in. 1. A sine wave y = k + A sin( Bx + C ) with A > 0 and B > 0 has amplitude 2, period 4 π , phase shift 3 π , and vertical shift 2. (a) What is the value of k ? (b) What is the value of A ? (c) What is the value of B ? (d) What is the value of C ? (e) Clearly label suitable scales on both axes and then sketch the sine wave over one complete period :

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2. This problem concerns the following graph. Note that the scales on the axes are not the same. 0 . 5 - 0 . 5 1 . 0 - 1 . 0 1 . 5 - 1 . 5 2 . 0 - 2 . 0 2 . 5 - 2 . 5 3 - 3 6 - 6 (a) What is the amplitude of this function? (b) What is the period of this function? (c) Write an equation of the form y = A cos( Bx ) that matches this graph. 3. Simplify the expression cos(

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Unformatted text preview: x ) + sin( x )tan( x ) to one trigonometric function. 4. Let α be an angle such that cot( α ) =-3 and cos( α ) < 0. (a) Which quadrant does α lie in? (b) Is csc( α ) positive or negative? (c) Use a fundamental identity to Fnd the exact value of csc( α ). (d) Use a fundamental identity to Fnd the exact value of sin( α ). 5. ±ind the exact value of sin ( φ + π 4 ) if sin( φ ) = 3 5 and cos( φ ) = 4 5 . ( Hint : sin ( π 4 ) = 1 √ 2 and cos ( π 4 ) = 1 √ 2 ) 6. Let β be an angle such that π < β < 3 π 2 and cos( β ) =-. 58. (a) Which quadrant does β/ 2 lie in? (b) Find the exact value of cos( β/ 2). (c) Find the exact value of sin( β/ 2). 7. Verify that sin( x )-cos( x ) sin( x )cos( x ) = sec( x )-csc( x ) . 15...
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Reworked Part (Exam2) - x sin x)tan x to one trigonometric...

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