Finding cos(2θ) When sin(θ) = 3/5

Trigonometry · Axiom Academy

EXAMPLE Finding cos(2θ) Using the Double-Angle Formula Learn to find cos(2θ) when given sin(θ) by applying the Pythagorean identity and double-angle formulas. Excellent work! You've successfully found cos(2θ) using the double-angle formula. Here's what we learned: Two-Step Process: To find cos(2θ), we first needed to find cos(θ) using the Pythagorean identity sin²(θ) + cos²(θ) = 1. Quadrant Matters: The sign of cos(θ) depends on which quadrant θ is in. Without additional information, we typically assume Quadrant I where all trig functions are positive. Three Double-Angle Formulas: There are three forms: cos(2θ) = cos²(θ) - sin²(θ), cos(2θ) = 2cos²(θ) - 1, and cos(2θ) = 1 - 2sin²(θ). Choose the most convenient one based on what you know! Strategic Choice: Since we knew sin(θ), using cos(2θ) = 1 - 2sin²(θ) was most efficient as it avoided needing to find cos(θ) for the double-angle calculation. This problem-solving strategy is crucial for trigonometry: identify what you need, find intermediate values using identities, then apply the appropriate formula. Practice with different quadrants to master the complete technique!

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