Question

exact value of cos (5pi/18-pi/9) ?

Answer 1

\[\frac{5 \Pi}{18} - \frac{\Pi}{9} = ?\]

Answer 2

5pi/18-2pi/18

Answer 3

Good. Subtract and simplify.

Answer 4

pi/6 ? I'm not sure how to find the exact value of this

Answer 5

Very good!

Cos(pi/6) is one of those values that you may or may not have been told to memorize at this point. If not, we can find it, as it's half the angle of pi/3.

So, if you don't have it memorized, but do have cos(pi/3) memorized, we can use the half-angle formula to find it.

Answer 6

Half-Angle Formula:
\[Cos^2 (\frac{\Theta}{2}) = \frac{1}{2}(1+Cos(\Theta))\]

Answer 7

cos 30 degrees? I believe it would be square root of 3 over 2

Answer 8

That's the one :)

Answer 9

If you already have that memorized, you're done. If not, you can show it by using the formula I posted, and Theta = pi/3

Answer 10

Thank you so much that was very helpful

Answer 11

Cos(pi/3) = 1/2

So:
\[Cos^2(\frac{\Pi}{6}) = \frac{1}{2}(1+Cos(\frac{\Pi}{3}) = \frac{1}{2}(1 + \frac{1}{2})\]

etc.

Answer 12

My pleasure :)

Answer 13

That makes sense now!