Suppose that alpha and beta are angles given as follows sin

Suppose that alpha and beta are angles given as follows: sin alpha = 3/5 and alpha is an angle in quadrant 2. cos beta = 60/61 and beta is an angle in quadrant 4. Compute the exact value of cos(alpha - beta).

Solution

Sin alpha=3/5 and alpha is in second quadrand and in second quadrant cosine is negative

Here opposite=3 and hypotenuse=5

Therefore adjacent=sqrt(25-9) =4

Cos alpha=-4/5

Cos beta=60/61

Here beta is in fourth quadrant and in fourth quadrant sin is negative

Adjacent=60 and hypotenuse=61

Opposite= 11

Sin beta=-11/61

Cos(alpha-beta)= cos alpha cos beta+sin alpha sin beta

=(-4/5)(60/61)+(3/5)(-11/61) =(-240/305)-(33/305)

=-273/305