# 2-4 - February 4 2005 Today 7.3 Trigonometric Substitution...

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February 4, 2005 Today § 7.3 Trigonometric Substitution 1

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Expression a 2 - x 2 Substitution x = a sin θ with - π 2 θ π 2 Identity 1 - sin 2 θ = cos 2 θ Useful relationships θ = arc sin x a cos θ = 1 - x a 2 tan θ = x a 2 - x 2
Expression x 2 - a 2 Substitution x = a sec θ = a cos θ with 0 θ < π 2 or π θ 3 π 2 Identity sec 2 θ - 1 = tan 2 θ

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Expression a 2 + x 2 Substitution x = a tan θ with - π 2
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