Use a calculator to find each value. Give answers as real numb...

Question

Use a calculator to find each value. Give answers as real numbers.

cos (tan⁻¹ 0.5)

Accepted Answer

Welcome back. I am so glad you're here. We are asked to determine the value of the expression by using a calculator round. Your answer to six decimal places. Our expression is the cosine of the inverse tangent of 0.8. Our answer choices are answer choice, A 0.780869. Answer choice B 0.686255 answer choice C 0.193347 and answer choice D 0.411089 right. The first thing we want to do is figure out if 0.8 is within the domain of our inverse tangent. And we recall from previous lessons and from the tables in the textbook that the domain of inverse tangent is from negative infinity to positive infinity. So yes, 0.8 is within that domain. We're good to go now that we've got the green light to proceed. This one's really neat because you can be in either degrees mode or radiance mode. Because what's inside here, our cosine function is an inverse tangent function which means that's an angle in there and whatever you put in. Actually, I recommend trying both ways in degrees modes, mode and radiance mode. You'll see you'll get the same answer. So go ahead and type in that cosine function into your calculator. It'll give you a set of parentheses and then use that inverse tangent button. It's the one that looks like tangent to the negative one, but that's not tangent to the negative one. It's inverse tangent. It'll give you another set of parentheses. Type in 0.8. Close both sets of parentheses hit enter and my calculator gets me as far as 0.780868809. We're going to the sixth decimal place. So that is going to be the third eight that looks to the fourth eight, the one next to it and it rounds up. So we'll have approximately 0.780869. And that is our answer. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Use a calculator to find each value. Give answers as real numbers.
cos (tan⁻¹ 0.5)

Key Concepts

Inverse Trigonometric Functions

Trigonometric Ratios

Calculator Functions

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