Question

how would i solve for the exact cos11pi/3

Answer 1

I'm assuming that you mean \(\cos \frac{ 11\pi }{ 3 }.\)

Answer 2

I'm not allowed a calculator for the exam

Answer 3

that's what i meant MathMale, sorry!

Answer 4

I'm assuming that you know that the cosine function is periodic, and that its period is 2Pi. The easiest way to approach this problem is to find an angle equivalent to 11Pi/3 that is between 0 and 2Pi. (Does that make sense to you?)

Answer 5

Yes, so do i need to find the degree version in order to do that?

Answer 6

the following is not necessarily the best way in which to do this, but let's just subtract 2p from 11Pi/3. One approach is to re-write 2Pi as 6Pi/3. You can check for yourself to ascertain that this really does equal 2Pi.

You could, of course, convert your angles to degrees, but it's totally unnecessary.

Answer 7

Keeping in mind that 2Pi = 6Pi/3, please subtract 2Pi from 11Pi/3.

In other words, subtract 6Pi/3 from 11Pi/3.

Answer 8

ok so thats 5pi/3 right?

Answer 9

that's perfect. Note that this 5pi/3 is less than 2Pi, so 5pi/3 IS in the interval [0, 2pi] as desired.

See if you can figure out in which Quadrant 5pi/3 lies.

Answer 10

Hint: 5pi/3 = 300 degrees.

Answer 11

quadrant 4!

Answer 12

Right on!
Now would you please draw that angle in Q4:

Answer 13

You can copy my drawing and then draw in the angle 2pi/3 = 300 deg.

Answer 14

Hint: 2pi/ 3 is just past 3pi/2 =270 degrees.