Question

given cos theta=-1/5 , pi 14 years ago

Answer 1

use the pythag identitiy:

cos^2 + sin^2 = 1

Answer 2

and since theta is in the 3rd quadrant, the sign of sin will be negative

Answer 3

what is theta though?

Answer 4

sin theta...

Answer 5

doesnt matter, you already know that value of cos regardless of theta

Answer 6

if we arrange the identity to solve for sin we get:

cos^2 + sin^2 = 1

sin^2 = 1 - cos^2

sin = sqrt(1-cos^2)

and since you already know cos, plug it in to determine sin

Answer 7

if the mathing method is a bit to abstract, we also have the option of simply drawing a circle and applying the trig definitions to it

Answer 8

sounds good.

Answer 9

cos = nextto/hyp so we apply the values given to the triangle about t

sin = over/hyp ; in this case sqrt(10-1)/5

and since we are confined to an area in the region where sin is negative; just make sure the end result has a negative sign attached to it

Answer 10

umm, 5^2 = 25 ... not 10 :)

Answer 11

sin = sqrt(25-1)/5 would definnatly be a better value