find the exact value for each function

tan pi/3

cos pi/4

pi/3 radians = 60º

so let's look at the 30,60, 90º right-angled triangle
the ratio of its sides is 1:√3:2
tan 60º = 1/√3
so tan pi/3 = 1/√3

in the same way pi/4 = 45º

consider the 45,45,90 triangle.
the ratio of its sides is 1:1:√2

take it from there.