How do you evaluate sin((5pi)/9)cos((7pi)/18)-cos((5pi)/9)sin((7pi)/18)?

1 Answer
Apr 16, 2016

1/2

Explanation:

This equation can be solved using some knowledge about some trigonometric identities. In this case, the expansion of sin(A-B) should be known:

sin(A-B)=sinAcosB-cosAsinB

You'll notice that this looks awfully similar to the equation in the question. Using the knowledge, we can solve it:
sin((5pi)/9)cos((7pi)/18)-cos((5pi)/9)sin((7pi)/18)
=sin((5pi)/9-(7pi)/18)
=sin((10pi)/18-(7pi)/18)
=sin((3pi)/18)
=sin((pi)/6), and that has exact value of 1/2