find the exact value

Question

sin α = 3/5 , − 3 π/2 < α < − π , tan β = − √ 3 , π/2 < β < π

a. sin (α + β)

b. cos (α + β)

c. sin (α - β)

d. tan (α - β)

Answer 1

This problem is intended to trip you up with signs, so BE CAREFUL!

The magnitude of the trig functions of angle a are sin 3/5, cos 4/5 and tan 3/4

The magnitude of the trig functions of angle b are sin sqrt(3)/2, cos 1/2 and tan sqrt(3).

Both angles are in quadrant 2.

Remember the mnemonic "AllSinTanCos" to tell you which function is positive in quadrant 1,2,3,4.

And angle b is measured in negative radians!

Now carefully use the addition formulae to get the answer...make sure you know in which quadrant the sum or difference angle falls!