sample-exam2 - α positive or negative(c Use a fundamental...

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Sample Exam for Exam 2 1. This problem concerns the following graph. Note that the scales on the axes are not the same. 0 . 1 0 . 1 0 . 2 0 . 2 0 . 3 0 . 3 0 . 4 0 . 4 0 . 5 0 . 5 2 2 4 4 (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. 2. Find the exact value of tan ( ψ + π 4 ) if tan( ψ ) = 3. It may help to remember that tan ( π 4 ) = 1.
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3. A sine wave y = k + A sin( Bx + C ) with A > 0 and B > 0 has amplitude 1 2 , period π , phase shift π 8 , and vertical shift 1 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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4. Let α be an angle such that tan( α ) = - 2 and sin( α ) > 0. (a) Which quadrant does α lie in? (b) Is sec(
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Unformatted text preview: α ) positive or negative? (c) Use a fundamental identity to Fnd the exact value of sec( α ). (d) Use a fundamental identity to Fnd the exact value of cos( α ). (e) Use a fundamental identity to Fnd the exact value of sin( α ). (f) Use a fundamental identity to Fnd the exact value of cos(-α ). 5. Let β be an angle such that 180 ◦ < β < 270 ◦ and cos( β ) =-. 64. (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). 6. Verify that cos( θ ) csc( θ )-sin( θ ) = tan( θ ) . 7. Verify that sin(3 x ) sin( x ) = 4 cos 2 ( x )-1 . Hint: To get started, write 3 x = 2 x + x ....
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sample-exam2 - α positive or negative(c Use a fundamental...

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