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

Step-by-step explanation:

slope = (y2 - y1)/(x2 - x1)

slope of WU = (4 - 1)/(2 - 0) = 3/2

slope of VU = (2 - 4)/(5 - 2) = -2/3

product of the slopes: 3/2 * (-2/3) = -1

The slopes of WU and VU are negative reciprocals since their product is -1.

Therefore, <U is a right angle.