Unformatted text preview: ndamental Identities 637 Solution.
1. According to Theorem 10.6, sec (60◦ ) =
2. Since sin 7π
4 √ =− 2
2, csc 7π
4 = 1
sin( 7π
4 ) 1
cos(60◦ ) . = Hence, sec (60◦ ) = 1
√
− 2/2 1
(1/2) = 2. √
2
= − √2 = − 2. 3. Since θ = 3 radians is not one of the ‘common angles’ from Section 10.2, we resort to the
calculator for a decimal approximation. Ensuring that the calculator is in radian mode, we
ﬁnd cot(3) = cos(3) ≈ −7.015.
sin(3) π
π
4. If θ is coterminal with 32 , then cos(θ) = cos 32 = 0 and sin(θ) = sin
sin(θ)
to compute tan(θ) = cos(θ) results in −1 , so tan(θ) is undeﬁned.
0 5. We are given that csc(θ) = 1
sin(θ) 3π
2 = −1. Attempting √
√
1
= − 5 so sin(θ) = − √5 = − 55 . As we saw in Section 10.2, we can use the Pythagorean Identity, cos2 (θ) + sin2 (θ) = 1, to ﬁnd cos(θ) by knowing sin(θ).
Substituting, we get cos2 (θ) + − √ 5
5 2 θ is a Quadrant IV angle, cos(θ) > 0, so cos(θ) =
6. If tan(θ) = 3, then si...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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