Find exact value of each expression
sec^-1 (2root3) / 5
I have no idea what to do to make that into a value. I know that sec^-1 is in quadrants one and two, but I'm not sure how to use that to solve the problem.
Thank you!
This is a trick question.
2√3/5 = 0.69
but sec(x) is never less than 1.
To find the exact value of the expression sec^-1(2√3)/5, we need to use the inverse function of secant, which is called the arcsecant (or sec^-1) function. The arcsecant function gives us the angle whose secant is equal to the input value.
First, let's find the angle whose secant is equal to 2√3. The secant function is the reciprocal of the cosine function, so we can express sec^-1(2√3) as cos^-1(1 / (2√3)).
Now, we need to evaluate this expression. To do that, use the fact that cos^-1(x) gives the angle whose cosine is x, and the range of cos^-1(x) is [0°, 180°]. So, we are looking for an angle between 0 degrees and 180 degrees whose cosine is equal to 1 / (2√3).
Using the cosine function, we know that cos(30°) = √3/2, which means cos^-1(√3/2) = 30°. Therefore, cos^-1(1 / (2√3)) = 30°.
Now, we can substitute this value back into the original expression:
sec^-1(2√3)/5 = (30° / 5) = 6°.
So, the exact value of the expression sec^-1(2√3)/5 is 6°.