Solve each equation for x.
arccos x + arctan 1 = 11π/12

Question

Solve each equation for x.

arccos x + arctan 1 = 11π/12

Accepted Answer

Hello, everyone. We are asked to find the exact solution of the equation. The arc cosine of X plus the arc tangent of radical three equals seven pi divided by 12. Our answer choices are A X equals one half BX equals radical two divided by two CX equals negative one half DX equals negative radical two divided by two. So I'm going to start by rewriting my equation. So I have the arc cosine of X plus the arc tangent of radical three equals seven pi divided by 12. So I'm gonna take this apart a little bit. I would first find the arc tangent of radical three. I wanna find out what does that equal? Well, I recall that if I wanted to rewrite this in another way, I could say this is the tangent of X equals radical three. So since it is positive, I know that it will probably be in the first quadrant since our range is in the quadrant one and quadrant two for tangent. So looking in quadrant one, I recall that tangent is sine divided by cosine. So the sine of X divided by the cosine of X. This would be when we have the square root of three divided by two divided by one half that would equal the square to three. And that occurs at the angle pi divided by three. So I can say that the arc tangent of radical three is pi divided by three. So I'm gonna plug that back into my equation. So the arc cosine of X plus pi divided by three equals seven pi divided by 12. And I'm going to isolate the arc cosine of X by subtracting pi divided by three from both sides. So I get the arc cosine of X equals and when I subtract this, we get pi divided by four. So again, I want to rewrite this a little bit. I recall the arc cosine is the inverse of the cosine. So this would be the cosine of pi divided by four has to equal our X value referencing a unit circle. I can find that the cosine of pi divided by four is the square root of two, divided by two. And that should be our value. Yep X will equal the square to two divided by two. And that's answer choice B have a nice day.

Struggling with Trigonometry?

Solve each equation for x.
arccos x + arctan 1 = 11π/12

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Inverse Sine, Cosine, & Tangent practice set

Struggling with Trigonometry?

Solve each equation for x.arccos x + arctan 1 = 11π/12

Watch next

Inverse Sine, Cosine, & Tangent practice set

Solve each equation for x.
arccos x + arctan 1 = 11π/12