Stitz-Zeager_College_Algebra_e-book

# The graph of y cosx is usually described as wavelike

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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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