Monday

April 21, 2014

April 21, 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

**Related Questions**

trig - I'm trying to see if the teacher didn't give us the right problem or if I...

Math(Please check) - 1) Use the cofunction identites to evaluate the expression ...

algebra-trig help asap - Evaluate the expression. Assume that all angles are in ...

Precal - Use a calculator to evaluate the expression. arcsin 0.45 arctan 15 ...

Math(Please check) - 1) Use the cofunction identites to evaluate the expression ...

Advanced Math I - If a * b = a - 3b and a # b = 2a + 3b, evaluate the expression...

math - Evaluate the expression without using a calculator. log under 2 1

Mathematics - How can I evaluate the expression below without using calculator? ...

trig - evaluate the following without using a calculator and please explain how ...

Trig - evaluate exactly(without calculator): 1. sec(pi/4) 2.3sin4pi 3. tan240(...