Comput: cos(sin−1(−60/61)+sin−1(40/41)=

Answer 1

the right triangle whose sine is -60/61

has opposite side 60, adjacent side of 11

per pythagorean theorem and hypotenuse 61.

Notice that 11^2 + 60^2 = 61^2

The sine is negative in quadrants 3 and 4, so

this angle is either 180 + inverse_sine(60/61) or

360 - inverse_sine(60/61)

which is ABOUT 260 or 280

The other right triangle has legs 9 and 40

and hypotenuse 41, since 9^2 + 40^2 = 41^2

The sine is positive in quadrants 1 and 2,

so this angle is either inverse_sine(40/41)

or 180- inverse_sine(40/41)

which is ABOUT 180 - 77.32= 102.68 or 77.32

So there are FOUR (4) possible sums of which

to find the cosine...

260 + 77.32

280 + 77.32

260 + 102.68

280 + 102.68

Finally, your parenthesis are unbalanced..

I am ASSUMING you want the cosine of the entire

expression as that is the only way it makes sense.