Question

Pls help me with this:

Find the exact value cos[2cos^-1(-1/2)]

Answer 1

\[\large \cos\left[2\color{orangered}{\arccos\left(-\frac{1}{2}\right)}\right]\]

Work from the inside out.
So what value does this arccosine give us?

\[\large \arccos\left(-\frac{1}{2}\right)=\theta \qquad\rightarrow\qquad \cos \theta=-\frac{1}{2}\]

Do you know what value of theta this gives us? :o

Answer 2

@zepdrix yes : 2pi/3 .... so what is the answer?

Answer 3

\[\large \cos\left[2\color{orangered}{\frac{2\pi}{3}}\right]\]

Ok good, you figured out the orange part.
Understand how to solve it from here? :)
You need to remember your special angles.

Answer 4

@zepdrix : so the answer is 4pi/3?

Answer 5

No. The inside simplifies to 4pi/3.
What does the cosine of 4pi/3 give you? :o

Answer 6

@zepdrix : -1/2

Answer 7

Yay good job \c:/

Answer 8

Oh I see! Thanks so much!