Solve each equation for exact solutions.
arccos x + 2 ar...

Question

Solve each equation for exact solutions.

arccos x + 2 arcsin √3/2 = π

Accepted Answer

Hello, everyone. We are asked to find the exact solution of the equation. The arc sine of X minus one half the arc cosine of radical three divided by two equals pi divided by four. Our answer choices are A X equals radical three divided by two BX equals negative radical two divided by two CX equals one half D no solution. So I'm going to rewrite arc sign and arc cosine as the inverse. So I have the inverse sine of X minus one half. The inverse cosine of radical three divided by two equals pi divided by four. So to begin, I'm going to use a unit circle and I'm going to find what is the inverse cosine of radical three divided by two. So when I do so I have the inverse sine of X minus one half and that's gonna be multiplied by the value of the inverse cosine of radical three divided by two which is pi divided by six. And this is gonna equal pi divided by four. Next, I'm gonna do the multiplication of my fraction. So I have the inverse sine of X minus and this will be pi divided by 12 equals pi divided by four to isolate the inverse sine of X. I'm gonna add pi divided by 12 to both sides. So I have the inverse sine of X equals and I need to make a common denominator. So I'll have three pi divided by 12 plus pi divided by 12. So we have the inverse sine of X equals four pi divided by 12, which is the same as pi divided by three. Move up here. So knowing that the inverse sine of X equals pi divided by three, I can look at this also as if it's saying the sine of pi divided by three equals X. And when I reference my unit circle, I find that X would have to equal radical three divided by two. So that is our answer. It's answer choice. A X equals the square to three divided by two. Have a nice day.

Struggling with Trigonometry?

Solve each equation for exact solutions.
arccos x + 2 arcsin √3/2 = π

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Inverse Sine, Cosine, & Tangent practice set

Struggling with Trigonometry?

Solve each equation for exact solutions.arccos x + 2 arcsin √3/2 = π

Watch next

Inverse Sine, Cosine, & Tangent practice set

Solve each equation for exact solutions.
arccos x + 2 arcsin √3/2 = π