How to Solve Identity Equations in Trigonometry

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How you will go about solving identity equations in trigonometry depends on exactly what you want to solve for. Solve identity equations in trigonometry with help from a mathematics educator in this free video clip.

Part of the Video Series: Trigonometry Education
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Hi, I'm Jimmy Chang and we're here to talk about how to solve identity equations in trigonometry. Now there's a lot of identity equations out there. Now when it comes to solving identity equations it really depends on what identity that you want to solve for. In other words what term you want to solve for specifically. So here's basically an example as to what I'm talking about. You're all aware of the Pythagorean Identity, sine square theta plus cosine square theta is equal to 1. Now what you want to think about is depending on where the directions are, what you want to solve for. Do you want to solve for sine or do you want to solve for cosine? Now suppose you want to solve for sine for example, what you want to think about is it's just like using Algebra, if you want to solve for sine, you want to get the sine on its own. So you want to subtract cosine squared on both sides. So you have sine squared theta is equal to 1 minus cosine squared theta and then, to solve for sine completely, because sine is squared, you want to take the square root of both sides. So you have sine of theta is equal to now, because the two terms are subtracted by each other, you really can't do too much with it algebraically but you do know since you're taking the square root of both sides it's plus or minus. So sine theta is equal to plus or minus square root of 1 minus cosine square theta. Now similarly speaking if your job was to solve for cosine theta you do the exact same thing, subtract both sides by sine squared and then take the square root of both sides. So the bottom line here is when it comes to solving identity equations in trigonometry, you want to be sure what it is that you're solving for which term that you want to isolate and then just use the Algebra and go from there. So I'm Jimmy Chang and this is a brief overview as to how to solve identity equations in trigonometry.

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