Evaluate each expression without using a calculator.
sin...

Question

Evaluate each expression without using a calculator.

sin (arccos (3/4))

Accepted Answer

Without using a calculator, determine the exact value of the expressions of arc cosine of five volts. And we have four possible answers B squared to seven divided by 12 squared of 13, divided by five squared of 119, divided by five and square root of 119 divided by 12. Now to solve this, we first need to create a triangle. We have arc cosine of five divided by 12. Now based on what we know about inverse trait functions, art cosine five divided by 12 will equal the, we can construct the triangle. Then with our side measures, we have theta here, we have five on the bottom and 12 as the IPO news because we know cosine data is equals to our adjacent side divided by our hypotenuse. Now, we can use this to find our son. We know sign data is our opposite side of our angle divided by our hypotenuse, which means we can denote our missing side as side A, this is equals to a divided by 12. Now, finally, since this is a right triangle, we can make use of the Python theorem which tells us that C squared is equals to A squared plus B squared, where C is our hypotenuse of the triangle. You can then write this as 12 squared equals A squared plus five squared, giving us 144 equals A squared plus 25. Simplifying, we get a squared equals 119 and we can take the square root to get A equals the square root of 119. Finally, we said S theta was a divided by 12, which means this is the square root of 119 divided by 12. If we look at our possible answers, we see the answer to this problem. Its answer. D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Evaluate each expression without using a calculator.
sin (arccos (3/4))

Key Concepts

Inverse Trigonometric Functions

Pythagorean Identity

Trigonometric Ratios

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