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.

tan (arcsin 0.12251014)

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. And then our expression is the tangent of the arc sign of 0.46382247. Our answer choices are answer choice. A 0.184224. Answer choice B 0.479863. Answer choice C 0.693453 and answer choice D 0.523544. All right. So we're taking the tangent of something and that something is the arc sign of a big number. Well, a long number, it's not very big. And arc sign we recall from previous lessons is the same as the inverse sign. So step one is we want to figure out if this 0.46382247 is within the domain of our inverse sign or arc sign. And we recall from previous lessons and from the tables in the textbook that the domain of inverse sign is from inclusive of negative one to positive one and this decimal does fall in between negative one and positive one. So we may proceed. Now, since you're entering this into a calculator, the first thing you want to figure out for the calculator is do you have to be in degrees mode or radiance mode? And actually, because arc sign, if something is an angle that you're putting in, you can be in either degrees mode or radiance mode. And actually, I encourage you to try both to see that you will get the same answer. So you'll plug in into your calculator tangent function. It'll give you a parentheses. And then you might have an arc sign button. I have an inverse sign button on mine that looks like sign to the negative one. That's not what it means, but that is the inverse sign button. I'll give you another parenthesis and then this might be the hardest part typing this incorrectly type in 0.463 82247. Then close both sets of parentheses hit enter and then my calculator got me as far as 0.523544106. But we're rounding to six decimal places. That's the second four looks to the one to the right of it and it remains a four. So we have approximately 0.523544. And that's our answer. We look at our answer choices and that matches with answer choice. D well done. We'll catch you on the next one.

Use a calculator to find each value. Give answers as real numbers.
tan (arcsin 0.12251014)

Key Concepts

Inverse Trigonometric Functions

Relationship Between Sine and Tangent

Use of Calculators for Trigonometric Values

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