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.

sin θ sec 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 expression is the cotangent of X multiplied by the Kant of X. Our answer choices are answer choice. A sine squared X divided by cosine X answer choice B cosine squared X divided by sine squared X answer choice C cosine X divided by sine X and answer choice D cosine X divided by sine squared X. All right. So we've got a cotangent and a co C can. And we need to get those in terms of sine and cosine. Let's start off with the cotangent. We recall from previous lessons that the cotangent of X is equal to the cosine of X divided by the sine of X. And hey, that is in terms of sine and cosine. So let's replace cotangent of X with its equivalent cosine of X divided by sine of X. All right. Now let's work on the koi can't of X. Well, cos can is a reciprocal function. We recall from previous lessons that Kant is the reciprocal function of the sine function. So Kan of X is equal to one divided by the sine of X. Let's replace Kan of X with one divided by sine of X. Now everything is in terms of sine and cosine and we can just multiply straight across and simplify, cosine of X multiplied by one in the numerators is just the cosine of X that's divided by, in the denominators sine of X multiplied by the sine of X is sine squared X. And there we go, 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.
sin θ sec θ

Key Concepts

Trigonometric Functions and Their Definitions

Expressing Functions in Terms of Sine and Cosine

Simplification of Trigonometric Expressions

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