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)/sec θ

Accepted Answer

Hello, everyone. We're asked to write the following trigonometric expression in terms of sine and cosine. We'll express our answer in terms of X only. We are given the cotangent of negative X divided by the kant of negative X. Our answer choices are a, the sine of XB, the cosine of XC, negative cosine of XD sine of X cosine of X. First rewriting our original expression, we have the cotangent of negative X divided by the KC can of negative X. Before I change these into sine and cosine, I'm gonna take into consideration our odd and even functions. So cotangent, we know the cotangent of negative X is equivalent to the negative cotangent of X and for kant of negative X that is equal to the negative kant of X. And since a negative divided by a negative is a positive, we now can work with this expression as the cotangent of X divided by the cosecant of X. So now let's convert this into sine and cosine. So cotangent of X is the same as the cosine of X divided by the sine of X. So that's our new numerator for a denominator. The kosi can of X is a reciprocal identity with sign. So this would be one divided by the sine of X. So we have the cosine of X divided by the sine of X in our numerator divided by one divided by the sine of X. In our denominator, I recall that there's a shortcut when I have a complex fraction that says if they have the same denominators, we can cancel the denominators out. And if we do so, here we get the cosine of X divided by one, which is the same as the cosine of X. And since that can't get any more simplified the cosine of X is our answer and that's answer choice. B have a nice day.

Struggling with Trigonometry?

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)/sec θ

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Introduction to Trigonometric Identities practice set

Struggling with Trigonometry?

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)/sec θ

Watch next

Introduction to Trigonometric Identities practice set

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)/sec θ