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September 2, 2014

September 2, 2014

Posted by **Chris** on Monday, May 18, 2009 at 8:34pm.

Evaluate the expression without the aid of a calculator.

arccos[(-3^1/2)/2)

I'm not sure how my teacher did it. I know she said to find which quadrant that cos can be in and graph the triangle to find the angle.

- trig -
**Reiny**, Monday, May 18, 2009 at 9:11pmfirst of all

3^(1/2) = √3

arccos[(-3^1/2)/2) really says :

find the angle theta, so that

cos theta = -√3/2

are you familiar with the ratio of sides of the 30-60-90 triangle ?

if so, then you should recognize that cos 30º = √3/2

but our cosine is negative so the angle must be in quadrants II or III by the CAST rule. (and 30º = pi/6 radians)

so theta is pi - pi/6 = 5pi/6

or

theta is pi + pi/6 = 7pi/6

then arccos[(-3^1/2)/2) = 5pi/6 or 7pi/6

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