08_3069_Key - MAC 1147 (3069) - Quiz #8 Name: Key For full...

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Unformatted text preview: MAC 1147 (3069) - Quiz #8 Name: Key For full credit, you must show all work and circle your final answer. 1 (1 point) In each group of two statements, circle the one that is always true. sec(−t) = sec(t) sec(−t) = − sec(t) csc(−t) = csc(t) csc(−t) = − csc(t) sec(−t) = sec(t) 2 tan(−t) = tan(t) tan(−t) = − tan(t) csc(−t) = − csc(t) tan(−t) = − tan(t) (2 points) If tan θ = 2, and θ lies in Quadrant I, find the exact value of 1 − cos2 θ 1 + cot2 θ . + 1 + tan2 θ 1 − sin2 θ 1 − cos2 θ sin2 θ = = tan2 θ, cos2 θ 1 − sin2 θ 1 + cot2 θ csc2 θ 1/(sin2 θ ) cos2 θ = cot2 θ. = = = 1 + tan2 θ sec2 θ 1/(cos2 θ ) sin2 θ So, 1 + cot2 θ 1 − cos2 θ + = (2)2 + 1 + tan2 θ 1 − sin2 θ = 4.25 = 3 2 1 2 = 4+ 1 = 4 17 4 (2 points) Find the value of the six trigonometric functions of θ with the given constraint: cos θ = 8 8 , 17 θ tan θ < 0. sin θ = − -15 17 cos θ = 15 17 8 17 tan θ = − 15 8 csc θ = − sec θ = 17 15 17 8 cot θ = − 8 15 University of Florida Honor Code: On my honor, I have neither given nor received unauthorized aid in doing this assignment. Signature ...
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