Question

how do i find sin5pi/2? detailed explanation please

Answer 1

Know your unit circle?

Answer 2

yea i have it in front of me

Answer 3

OK. So, where on there is the angle \(\dfrac{5\pi}{2}\)?

Answer 4

i only see pi/2 and 3pi/2

Answer 5

I start at 0 and count out \(\dfrac{\pi}{2}\) as I go around.

0

\(\dfrac{\pi}{2}\)

\(\dfrac{2\pi}{2} = \pi\)

\(\dfrac{3\pi}{2}\)

\(\dfrac{4\pi}{2} = 2\pi\)

\(\dfrac{5\pi}{2}\)

So where does that land on the circle?

Answer 6

on pi/2 so its 1?

Answer 7

Yes.

Answer 8

thank you very much!!!!

Answer 9

No problem. At some point you should hear about reference angles. That is the simplest angle that has the same measure or a related measure. Another, related, concept is coterminal angles. Those are angles that have the same terminal.

Because \(\dfrac{\pi}{2}\) and \(\dfrac{5\pi}{2}\) land at the same place, they are coterminal angles. \(\dfrac{\pi}{2}\) also happens to be the reference angle for \(\dfrac{5\pi}{2}\) (which is not always the case.)

Answer 10

how would i do sin-pi/2?

Answer 11

ok so it woud be -1?

Answer 12

Yep. I think you are getting it. You just go in the correct direction until you land on the angle, then use x, y, or both as needed to find the sine, cosine, tangent, etc.

Answer 13

ok so i understand the sine ones. Are the cosine ones different?

Answer 14

\(\sin \theta = y\)

\(\cos \theta = x\)

\(\tan \theta = \dfrac{y}{x}\)

Answer 15

Note that causes some problems for tangents on the y axis. It would be division by 0.