Question

Identify the coterminal angle between 0 and 2π. Then evaluate the function:Cos 19π/3

Answer 1

Step 1) use a calculator to compute the approximate value of `19pi/3`. Is the result between 0 and 6.28 ? If so, then the angle is already between 0 and 2pi. If not, then jump to step 2

step 2) If the angle is larger than 6.28, then subtract off 2pi. Then jump back to step 1 (but instead of 19pi/3, it would be this new angle)

Answer 2

hopefully that makes sense?

Answer 3

Okay.So I did 19/3 and got 6.3 then subtracted 6.28 and got 0.02,I'm confused on what to do next.

Answer 4

19pi/3 = 19.8967534727353 is not between 0 and 6.28

so we subtract off 2pi

(19pi/3) - (2pi)

(19pi/3) - (6pi/3)

(19pi - 6pi)/3

13pi/3

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so the angles 19pi/3 and 13pi/3 are coterminal angles

Answer 5

is 13pi/3 between 0 and 2pi? let's find out

13pi/3 = 13.6135681655558
so the answer is no

we have to subtract off 2pi again

we keep this going until we find an angle between 0 and 2pi (6.28)

Answer 6

what is `(13pi/3) - (2pi)` equal to in terms of pi?

Answer 7

7.3π?

Answer 8

13pi/3=13.6-2pi=7.32

Answer 9

\[\Large \frac{13\pi}{3} - 2\pi\]

\[\Large \frac{13\pi}{3}-\frac{6\pi}{3}\]

\[\Large \frac{13\pi-6\pi}{3}\]

\[\Large \frac{7\pi}{3}\]

So 13pi/3 and 7pi/3 are coterminal. Hopefully you agree with the steps?

Answer 10

Ohhhh yes I understand it. Thank you so much for the help!

Answer 11

no problem