Use a calculator to approximate the value of each expression. ...

Question

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

1/csc(90°-51°)

Accepted Answer

Welcome back. I am so glad you're here. We're asked to evaluate the following trigonometric expression using a calculator. Approximate the answer to four decimal places. We are given the trigonometric expression one divided by the C can of 90 degrees minus 43 degrees. Our answer choices are answer choice. A negative 0.0082 answer choice B negative 0.0125 answer choice, C 0.6820 and answer choice D 0.7314. All right. This is exciting because it says use the calculator. But my calculator doesn't have ac can't function button. But we do know that C is a reciprocal function. We know that the cosine of X equals one divided by the CC of X. And look, we're already in that format. We have the one divided by the CC of, in our X. Here is the 90 degrees minus 43 degrees. So we can just set our fraction equal to the cosine of instead of X, we have the cosine of 90 degrees minus degrees. OK? I can do the cosine of 90 degrees minus 43 degrees. On my calculator first. What's 90 degrees minus 43 degrees? That's 47 degrees. So cosine of 47 degrees. Now, very important, make sure that you are in degrees mode in your calculator. And if you are, you plug that in, you'll get an answer of 0.68199836. Your calculator might have more numbers than that, but we're asked to round to four decimal places. So after the decimal point, the fourth one is the first nine here that nine looks to the nine next to it and it gets to round up. So that's going to round us up to 0.6820. And there is our answer. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.
1/csc(90°-51°)

Key Concepts

Reciprocal Trigonometric Functions

Co-Function Identity

Using a Calculator for Trigonometric Values

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