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Calculus and Beyond Homework Help
Trig Substitution: Solving Homework Equations
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[QUOTE="arildno, post: 4523528, member: 8040"] It is a good exercise to derive the simplified expressions of trigs with inverse trigs as their arguments. For example, let's take cos(asin(x)). Not bothering about the precise domain for the inverse trig right now, we know that we have the identity: [tex]\cos^{2}(asin(x))+\sin^{2}(asin(x))=1[/tex] But, the latter term on the LHS simplifes to x^2! Thus, we have: [tex]\cos(asin(x))=\pm\sqrt{1-x^{2}}[/tex] This is also readily seen geometrically: If we look at a right-angled triangle with unit hypotenuse, and sine equal to x (to which the relevant angle is asin(x)), then that expression falls right out of the Pythagorean theorem. [/QUOTE]
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Trig Substitution: Solving Homework Equations
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