Barron's Math IIC SAT Subject Test Page 82
Which of the following is a solution of cos3x=0.5
a) 60 degrees
b) (5pi)/3
c)cos^-1 (1/6)
d) cos^-1 ($\displaystyle \frac{\sqrt3}{2}$
e)$\displaystyle \frac{1}{3}$cos^-1(1/2)
Barron's Math IIC SAT Subject Test Page 82
Which of the following is a solution of cos3x=0.5
a) 60 degrees
b) (5pi)/3
c)cos^-1 (1/6)
d) cos^-1 ($\displaystyle \frac{\sqrt3}{2}$
e)$\displaystyle \frac{1}{3}$cos^-1(1/2)
It depends on the problem.
If you had $\displaystyle \sin (x+3)=\tfrac{\sqrt{3}}{2}$, and you wanted to solve for x, you would apply arcsin to both sides, since we know that $\displaystyle \sin^{-1}\left(\sin u\right)=u$
In your problem, you would have to apply arccos to both sides, since we know that $\displaystyle \cos^{-1}\left(\cos u\right)=u$
Does this clarify things?
--Chris