In Exercises 47–54, use the figures to find the exact value of ea...

Question

In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θ θ2 sin ------- cos -------2 2

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the trigonometric function. Using the provided figure, the value we are looking for is of the function two sine of beta divided by two cosine beta divided by two. We are given a right triangle pr Q with the right angle at R and the angle beta at Q. Our hypotenuse is 10 side pr measures eight and side QR measures six, we are given four answer choices. A 3/5 B 4/ C five halves D five thirds. All right. So thinking back to what we are given, we are given two multiplied by the sign of beta divided by two multiplied by the cosine of beta divided by two. This looks very similar to the formula that we have when we're working with a double sign angle. If you recall that formula was that the sign of two, theta equals two multiplied by the sign of theta cosine of theta. Since this looks very similar, we could say that in this case, theta is equal to beta divided by two. So if that is the case, we are gonna substitute in beta divided by two in the sign of two theta. So we are gonna say that two sign B are divided by two cosine beta divided by two would be equal to the sign of two multiplied by beta divided by two. So now that we know this, we're gonna simplify the sign of two multiplied by beta divided by two. And that would be the sign of beta. So recall that sign is the opposite over the hypotenuse. So the sign is gonna be the sign of beta is the opposite side pr divided by the Hippo Q P. The value of pr is eight, the value of Q P is 10, this would reduce to 4/5. So the sign of beta is 4/5. And we now can say that the exact value of two multiplied by the sign of beta divided by two cosine beta divided by two equals 4/5. So 4/5 is our answer and is answer choice B have a nice day.

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In Exercises 47–54, use the figures to find the exact value of each trigonometric function.θ θ2 sin ------- cos -------2 2

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