Use identities to correctly complete each sentence.

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Question

Use identities to correctly complete each sentence.

If cos θ = 0.8 and sin θ = 0.6, then tan(-θ) = ________________.

Accepted Answer

Hello, everyone. We are asked to find the exact value of the tangent of negative theta. If the sine of theta equals 0.28 and the cosine of theta equals 0.96. Our answer choices are a negative 25 divided by seven B seven, divided by 24 C 25 divided by seven D negative seven divided by 24. First recall that with odd and even functions, I can say that the tangent of negative theta is equal to the negative tangent of theta. So I'm going to rewrite it like that. And then I recall that tangent is the same as S divided by cosine. So this can be rewritten as the negative. And then in parentheses, sine of the divided by cosine of the. This is what I'm gonna use to plug the values in. So the negative sine of theta divided by cosine of theta in parentheses, using the decimals we're given, we have negative and then in parentheses, 0.28 divided by 0.96. Because all my answer choices are division with non decimal numbers. I want to make this into a non decimal number. Before I try to reduce, I'm going to do that by multiplying both the numerator and the denominator by 100. And when I do so, I have negative and in parentheses 28 divided by 96 this will make it a lot easier to reduce. So looking at 28 and 96 I recognize they both can be reduced by four. So I'm dividing the numerator and denominator by four. My negative stays put. And then in the parentheses, 28 divided by 47, 96 divided by four is 24. So I have negative 7 24th which is the same as saying negative seven divided by 24 which is answer choice D and our exact value have a nice day.

Use identities to correctly complete each sentence.

If cos θ = 0.8 and sin θ = 0.6, then tan(-θ) = ________________.

Key Concepts

Trigonometric Ratios

Even-Odd Identities

Using Given Values to Find Tangent

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