Show how you could set up and find the exact value of cos (5π/4) in two different ways.

note that 5π / 4 is in the third quadrant where the cos is negative

the related acute angle to 5π / 4 is π/4, thus

cos (5π / 4) = - cos (π/4) = - √2/2

We can also evaluate using the addition formula for cosine

• cos (x + y) = cosxcosy - sinxsiny

note that 5π / 4 = (π + π/4)

cos (5π / 4) = cos (π + π/4)

= cos (π) cos (π/4) - sin (π) sin (π/4)

= - 1 √2/2 - 0 = - √2/2