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:
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This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.
 Summer '08
 GERMAN
 Calculus

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