Write each function value in terms of the cofunction of a comp...

Question

Write each function value in terms of the cofunction of a complementary angle.

sin (2π/5)

Accepted Answer

Welcome back, everyone. In this problem, we want to figure out which of the following core functions has the same value as the sine of 1/9 of Pi. For our answer choices. A says it's the cosine of 1/9 of pi B says it's the cosine of 7/18 of Pipi. C says it's the sine of 7/18 of Pi and D the tangent of 7/18 of Pi. Now we're trying to figure out the core function that has the same value as the sine of 1/9 of Pi. And recall that the core function identity relates trigonometric functions. So what do we know about the core function identity for sine? Well, recall that the core function identity for a sine tells us that the sine and cosine functions are complementary. In other words, the sine of theta would be equal to the cosine of 90 degrees. Or in this case, since we're looking at our angling radiance, a half of pi minus 30 degrees, so both our angles should sum to a half of pi. No, that means since we know our anger is 1/9 of Pi, then this tells us that the sign of 1/9 of pi is going to be equal to the cosine of a half of pi minus 1/9 of pi. So if we can figure this out, then we'll figure out our cosine coun. Now let's figure this out by writing them with common denominators. Now, two and nine have 18 as the lowest common multiple. So we can write 18 as the new denominator two goes into 18, 9 times and nine multiplied by pi equals nine pi where nine goes into 18, 2 times and the two multiplied by pi equals two pi nine pi minus two pi equals seven pi. Therefore, that tells us that the sine of 1/9 of pi is going to be the same thing as the cosine of 7/18 of pi. If we look back on our answer choices, that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

Write each function value in terms of the cofunction of a complementary angle.
sin (2π/5)

Key Concepts

Cofunction Identities

Complementary Angles

Unit Circle

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