Find the exact value of each expression. (Do not use a calcula...

Question

Find the exact value of each expression. (Do not use a calculator.)

cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the following trigonometric function without using a calculator. We are given the cosine of five pi divided by 11, multiplied by the cosine of six pi divided by 11 minus the sine of five pi divided by 11 multiplied by the sine of six pi divided by 11. Our answer choices are a zero B one C negative one D two. So to begin with what we are given as a trig function reminds me a lot of an identity that we've been using and that identity is the sum of angles of a cosine. So that identity states that the cosine of X plus Y equals the cosine of X multiplied by the cosine of Y minus the sine of X multiplied by the sine of Y. And when I match those up, that appears to be what I have here where X has a value of five pi divided by 11 and Y has a value of six pi divided by 11. So let's work backwards. We're gonna put that in the part where it says the cosine of X plus Y, we'll have the cosine of five pi divided by 11 plus six pi divided by 11. When I add those together, I get the cosine of 11 P divided by 11, which can be reduced to the cosine of pi. And then when I reference a unit circle, the cosine of pi has a value of negative one. So in the end, our answer here is negative one and that's answer choice C have a nice day.

Struggling with Trigonometry?

Find the exact value of each expression. (Do not use a calculator.)
cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)

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Struggling with Trigonometry?

Find the exact value of each expression. (Do not use a calculator.)cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)

Watch next

Sum and Difference Identities practice set

Find the exact value of each expression. (Do not use a calculator.)
cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)