Use the given information to find each of the following.

Question

sin x, given cos 2x = 2/3 , with π < x < 3π/2

Accepted Answer

Hello, everyone. We are asked to determine the exact value of the given trigonometric expression using the half angle identity. We're asked to find the sine of X. If the cosine of two X equals 4/9 and X is located between pi and three pi divided by two, our answer choices are a negative radical 10 divided by three B radical 10 divided by three C negative radical 10 divided by six D radical 10 divided by six. So first, if we are looking for the sine of X and asked to use a half angle identity, I'm gonna take that the sign of a divided by two is the half angle identity that will give me plus or minus the square root of one minus the cosine of a divided by two. Since we're provided the cosine of two X is 4/9. This is the right half angle identity for us. So A is gonna be two X half of A will be X. So we'll say that the sign of X equals and it's plus or minus. But this tells me we're in quadrant three, which means our sign will be negative. So then we have the square root of one minus our cosine of A which will be 4/9 divided by two. So the sin of X equals negative square root one minus 4/9 is 5/9 divided by two. And when I do that, I will get negative square root of 5/18 because 5/9 divided by two will give me 5/18 simplifying my radical, I have a negative still on the outside and my numerator will be the square of five. My denominator will be the square root of 18. I'm gonna simplify my denominator. So I still have negative out front squared of five divided by this can be simplified to three radical two. I want to rationalize my denominator by multiplying numerator and denominator by the square root of two. So I have the negative square root of 10 divided by six. And that is as simplified as it can get. So our S equals negative square root of 10 divided by six. And that is answer choice C have a nice day.

Struggling with Trigonometry?

Use the given information to find each of the following.
sin x, given cos 2x = 2/3 , with π < x < 3π/2

Watch next

Double Angle Identities practice set

Struggling with Trigonometry?

Use the given information to find each of the following.sin x, given cos 2x = 2/3 , with π < x < 3π/2

Watch next

Double Angle Identities practice set

Use the given information to find each of the following.
sin x, given cos 2x = 2/3 , with π < x < 3π/2