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

Question

Evaluate each expression without using a calculator.

cos (csc⁻¹ (-2))

Accepted Answer

Without using a calculator, determine the exact value of the expression cosine of co seeking inverse of negative spirits of two. With four possible answers being the spirit of two divided by two negative spirits are two divided by two, one half and the square of three divided by two. Now, to solve this, we first need to use a trick property to modify go seeking inverse. If we have cos inverse of sum value X, we can rewrite this as sine and verse one divided by that value X, we could then write this as sine inverse one divided by negative square root of two, which can also be rationalized as sine inverse, negative squares of two divided by two. Now the range of sine inverse we should know goes to negative pi divided by two, two pi divided by two. So if we look at our unit circle on the right here, we need to find an angle on the right side of our unit circle with our sign value negative squares of two divided by two, we can see that this occurs at the angle seven pi divided by four. Now because our d our range restriction we should say it's some negative pi divided by 22 pi divided by two. This angle transformed into negative pi divided by four. We can now replace our coking inverse negative squares of two. We will say K inverse negative square root of two equals negative pile of is by four, which means we have cosine of negative pi divided by four. Finally, if we look again at our unic circle, the cosine of negative pi divided by four is a square root of two divided by two. We can then see the answer to our problem is answer a OK. Hope to help you solve the problem. Thank you for watching. Goodbye.

Evaluate each expression without using a calculator.
cos (csc⁻¹ (-2))

Key Concepts

Cosecant and Inverse Cosecant

Trigonometric Ratios

Cosine Function

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