if sinx=7/5 and angle x is in quadrant 2 and cos y=12/13 and angle y is in quadrant 1 find sin (x+y)

Question

please Help

Answer 1

First of all, sinx = 7/5 is not possible because the opposite side (7) should not be longer than the hypotenuse (5), unless this should have been sinx = 5/7.

So, instead if we just use sinx = 5/7 in quadrant II:

x = arcsin(5/7) = 45.58 degrees (this is the reference angle), so

x = 180 - 45.58 = 134.42 degrees

Then cos y = 12/13 in quadrant I:

y = arccos(12/13) = 22.62 degrees

Therefore,

sin (x + y) = sinx cosy + cosx siny

                = sin 134.42 cos 22.62 + cos 134.42 sin 22.62

                = (0.7142)(0.9231) + (-0.6999)(0.3846)

                = 0.6593 - 0.2692

                = 0.3901