Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
cos θ = 0.16

I know how to find the answers when it's in fraction form, however, I do not know how to do it when the problem is in decimals. Is it correct to put the decimal into fractions or would that be wrong? Please help!

Answer 1

fractions are just numbers. Why is it any easier to find θ if

cosθ = 4/25

?? You still have to evaluate cos^-1(x) using your calculator. Seems to me that using a decimal is even easier than using fractions.

Now, if you have some problem like

sin(arccos(.16)) then it would seem reasonable to use a fraction, since then it is clear that if

cosθ = 4/25,
sinθ = √84/25

Answer 2

I know how to find the answer with a fraction because those usually come out to become a 30-60-90 or 45-45-90 triangles. Or if they don't I use the pythagorean theorem to find the unknown side and figure out the problem that way.

But I figured it out. The answer was 1.41+2pi(k),4.87+2pi(k).