Stitz-Zeager_College_Algebra_e-book

Verify the domains and ranges of the tangent cosecant

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Unformatted text preview: ). If, in addition, we know where the terminal side of θ lies when in standard position, then we can remove the ambiguity of the (±) and completely determine the missing value as the next example illustrates. Example 10.2.2. Using the given information about θ, find the indicated value. 3 1. If θ is a Quadrant II angle with sin(θ) = 5 , find cos(θ). √ 2. If θ is a Quadrant III angle with cos(θ) = − 5 5, find sin(θ). 3. If sin(θ) = 1, find cos(θ). Solution. 1. When we substitute sin(θ) = 3 into The Pythagorean Identity, cos2 (θ) + sin2 (θ) = 1, we 5 9 4 obtain cos2 (θ) + 25 = 1. Solving, we find cos(θ) = ± 5 . Since θ is a Quadrant II angle, its terminal side, when plotted in standard position, lies in Quadrant II. Since the x-coordinates are negative in Quadrant II, cos(θ) is too. Hence, cos(θ) = − 4 . 5 √ √ 2 2. Substituting cos(θ) = − 55 into cos2 (θ) + sin2 (θ) = 1 gives sin(θ) = ± √5 = ± 2 5 5 . Since θ is a Quadrant III angle, both its s...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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