Write each expression in terms of sine and cosine, and then si...

Question

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.

tan θ cos θ

Accepted Answer

Welcome back. I am so glad you're here. We are asked to write the following trigonometric expression in terms of sine and cosine express your answer in terms of X. Only our given trigonometric expression is the cotangent of X multiplied by the cosine of X. Our answer choices are answer choice. A cosine squared X answer choice B cosine X divided by sine X, answer choice C sine X divided by cosine squared X and answer choice D cosine squared X divided by sine X. All right. So we want it in terms of sine and cosine. Half of it's already in cosine, but half of it isn't, let's take a look at this cotangent of X will come off to the side and see if we can get the cotangent of X in terms of sine and cosine. Well, we remember from previous lessons that the cotangent of X is equal to the cosine of X divided by the sine of X. And so here because those two are the same thing we can substitute in for the cotangent of X, what it's equal to which is the cosine of X divided by the sine of X. So let's just replace the cotangent of X with the cosine of X divided by the sine of X. And then don't forget that that is being multiplied by the cosine of X. When we just do this multiplication and combine it in the numerator cosine of X multiplied by the cosine of X is the cosine squared of X. And that's divided by the sine of X. And we've written our trigonometric expression in terms of sine and cosine. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
tan θ cos θ

Key Concepts

Definition of Tangent in Terms of Sine and Cosine

Multiplication and Simplification of Trigonometric Expressions

Expressing Functions in Terms of a Single Variable

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