In Exercises 1–26, find the exact value of each expression. _ ...

Question

In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ (−√3)

Accepted Answer

Hello everybody I doing today. Then we're going to be looking at this question that states for the following trigonometric expression evaluate and give the answer as an exact value in radiance where the expression is inverse tangent of negative one. Now the extras provided are a negative pi divided by two B negative pi divided by three C negative pi divided by four and D negative pi divided by six. Now for this question, let's say that if inverse tangents of negative one or first, let's say inverse tenant of positive one. So let's say if inverse 10 of positive one is equal to X, then tangent of X is equal to one. And this will become valuable later on. Now this is just a way of how to move from inverse tangent to regular tangent. Now let's rewrite our expression. So our expression was that inverse tangent of negative one and we can rewrite that as negative inverse tangents of positive one. And this is why this the what we said earlier is valuable because now we are, if we ignore the negative, we are at inverse tenure a positive one. So now we can recall that tangent of 45 degrees is equal to one. Therefore, we have the, the inverse tangent of negative one as equal to negative inverse tangent of one which is equal to negative degrees because we have that 10 year of 45 equals one. So inverse tangent positive inverse tangent of one is 45. So now 45 degrees. So now we add the negative in front and we'll have negative 45 degrees and now we have it in degrees. We can convert to radiance and we'll have open parentheses, negative 45 degrees closed parentheses multiplied by open parentheses, pi divided by 180 degrees closed parentheses. And this will come out to a negative pi divided by four. And that will be the answer to our question. So we'll have that inverse tangents of negative one is equal to negative pi divided by four which matches with Andresa C. And we can see how valuable it is to be able to recall different values uh tangents sign and so on how important it is to be able to recall different trigonometric function values from our unit circle values that we should know right away. So I hope that was helpful. And until next time.

In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ (−√3)

Key Concepts

Inverse Tangent Function (tan⁻¹ or arctan)

Exact Values of Tangent for Special Angles

Handling Negative Arguments in Inverse Trigonometric Functions

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