In Exercises 39–54, find the exact value of each expression, if p...

Question

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator.

sin⁻¹ (sin 5π/6)

Accepted Answer

Hello, today we're gonna be determining the exact value of the following trigonometric expression. So what we are given is sine inverse of sine of two pi over three. Now there is one property for trigonometric functions that is going to help us simplify this expression whenever we multiply a trigonometric function to its respective inverse or we multiply the inverse of a of a trigonometric function to its respective function. What is going to happen is that the product of a trigonometric function and its inverse is going to cancel out the trigonometric function. And what we are left with is just the inside angle. This property is true for all six of the trigonometric functions. And so if we utilize this property on the given expression sine inverse multiplied by sine is going to cancel each other out leaving us with the inside angle which is going to be two pi over three and two pi over three is going to be the exact value of the given expression. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem and I'll go ahead and see you all in the next video.

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In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin⁻¹ (sin 5π/6)