Question

To solve equations involving inverse sin, cos, and tan such as cos(3x) = -7/10 do I need to use a calculator or is there a way to do it by hand?

Answer 1

So you would take \[\cos^{-1} \cos(3x) =\cos^{-1} (\frac{ -7 }{ 10 })\]
to get
\[3x=\cos^{-1} (\frac{ -7 }{ 10 })\]
is there a way to find x as a fraction by hand? Or is it necessary to use a calculator for the \[\cos^{-1} \]

Answer 2

Yes, you'll need a way to approximate. Only for certain angles will you be able to know the angle. The easy ones are 0,30,45,60,90 and multiples of these. -7/10 is not one that has an easy-to-memorize angle associated with it. What calculators to is approximate using tools like the Taylor series expansion of the function. If you want to do by hand, you can approximate using that kind of technique.

Here are some of the easy ones that you don't need special tools to find the angles:
http://en.wikipedia.org/wiki/30-60-90#30.E2.80.9360.E2.80.9390_triangle

Answer 3

Ok thanks for the help! Cramming all of Precalc into a week and found that the trig portion is the hardest part xD

Answer 4

It can be challenging. Remember as many identities as you can and try to use them where you can, it will save lot's of time trying to derive them. Worst case, know how to derive some of the most common. But certainly remember cos A + B , sin A + B and all the half-angle formulas. They are very common.

Answer 5

Awesome thanks!

Answer 6

NP