How to Get Rid of an Inverse Sine in an Equation

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Getting rid of an inverse sine in an equation may be required to complete certain types of problems. Get rid of an inverse sine in an equation with help from a longtime mathematics educator in this free video clip.

Part of the Video Series: Trigonometry & Other Math
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Hi, I'm Jimmy Chang, and we're here to talk about how to get rid of an inverse sign in an equation. Now when it comes to inverse signs they're a very useful tool but sometimes it might be necessary to get rid of them in an equation depending on what it is that you're solving for. So here's how you basically do that. Suppose you have an equation theta is equal to sin inverse of X. Now, you have an inverse sin here. Now to get rid of an inverse sin what you do is you literally you take the sin of both sides so here's how that works. You're going to have a sin of theta is equal to sin of sin inverse of X. Now sin and inverse sin are opposite operations or inverse operations of each other so the idea here is you're going to keep the sin of theta but sin and sin inverse literally cancel each other out and you're left with X. Now the same way happens if you have an arc sin. Arc sin and sin inverse have the same kind of notation so if you have an equation of theta is equal to arc sin of X, since it has the same notation as sin inverse you take the sin of both sides. So you have sin theta is equal to sin, arc sin of X and this cancels so you're left with sin theta is equal to X. So the bottom line is to get rid of an inverse sin you take the sin of both sides of the equation and you'll be fine. So, I'm Jimmy Chang, and that's how to get rid of an inverse sin in an equation.

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