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Unformatted text preview: MAC 1147 (4258)  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.
cos(−t) = cos(t)
cos(−t) = − cos(t) sin(−t) = sin(t)
sin(−t) = − sin(t) cos(−t) = cos(t) sin(−t) = − sin(t) cot(−t) = cot(t)
cot(−t) = − cot(t)
cot(−t) = − cot(t) (2 points) If csc θ = 5, and θ is an acute angle, ﬁnd the exact value of
1 + cot2 θ +
1 + cot2 θ = √ csc2 θ = csc θ, So,
1 + cot2 θ + 1
cos θ
+
.
cot θ 1 − cos2 θ cos θ
cos θ
=
= sin θ,
cot θ
(cos θ )/(sin θ ) 1
1
1
cos θ
+
= 5 + + 25 = 30 +
=
2θ
cot θ 1 − cos
5
5
= 30.2 = 3 1
1
=
= csc2 θ.
2θ
1 − cos
sin2 θ 151
5 (2 points) Find the value of the six trigonometric functions of θ with the given constraint:
csc θ = 4, cot θ < 0. sin θ = 4
1
θ
√
− 15 1
4 csc θ = 4 √
15
cos θ = −
4 4
sec θ = − √
15 1
tan θ = − √
15 √
cot θ = − 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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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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