Solve each equation for exact solutions.
6 sin⁻¹ x = 5π

Question

Solve each equation for exact solutions.

6 sin⁻¹ x = 5π

Accepted Answer

Hey, everyone here we are asked to find the exact solution of the equation four multiplied by sine inverse of X is equal to three multiplied by pi. Here we have four answer choice options. A X is equal to negative square root of two BX is equal to negative one, divided by two CX is equal to negative square root of three divided by two and answer D no solution. So before we can find the exact solution of the equation, we first need to solve the equation for X. So the first step is to get rid of the coefficient of the sine inverse function. And so that means we have to divide both sides of the by the coefficient which is four. So we divide both sides by four and this gives us sine inverse of X is equal to three multiplied by pi divided by four. And now, before we continue solving four, X, we just first want to recall the range for the sine inverse function. And so the range is open bracket, negative pi divided by two to po positive pi divided by two and closed bracket. So both of these values are included And now looking at our equation so far, we notice again, we have sin inverse of X is equal to three multiplied by pi divided by four. And while we can realize here that the value on the right hand side is not within the range, so that tells us that this equation is just not possible here, we cannot solve for X. And therefore, we know again since this value is not within the range that we have no solution, so we can stop here in solving. And we are left with answer choice D where again, we have no solution. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Struggling with Trigonometry?

Solve each equation for exact solutions.
6 sin⁻¹ x = 5π

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Struggling with Trigonometry?

Solve each equation for exact solutions.6 sin⁻¹ x = 5π

Watch next

Inverse Sine, Cosine, & Tangent practice set

Solve each equation for exact solutions.
6 sin⁻¹ x = 5π