Angle x is in the second quadrant and angle y is in the first quadrant such that sinx=5/13 and cosy=3/5.

a) Determine an exact value for cosx
b) Determine an exact value for siny

To determine the exact values for cosx and siny, we can use the Pythagorean identity and the given information about sinx and cosy.

a) To find the exact value of cosx:
In the second quadrant, the sine is positive, and the cosine is negative. We know that sinx = 5/13, so we can use the Pythagorean identity to find the value of cosx:

cosx = sqrt(1 - sin^2(x))
cosx = sqrt(1 - (5/13)^2)
cosx = sqrt(1 - 25/169)
cosx = sqrt((169 - 25)/169)
cosx = sqrt(144/169)
cosx = 12/13

Therefore, the exact value of cosx is 12/13.

b) To find the exact value of siny:
In the first quadrant, both sine and cosine are positive. We know that cosy = 3/5. From the Pythagorean identity, we can find the value of siny:

siny = sqrt(1 - cos^2(y))
siny = sqrt(1 - (3/5)^2)
siny = sqrt(1 - 9/25)
siny = sqrt((25 - 9)/25)
siny = sqrt(16/25)
siny = 4/5

Therefore, the exact value of siny is 4/5.