The functions above are two trigonometric functions f and g

The functions above are two trigonometric functions f and g graphed over one period. Assuming we are just looking at the one period, find the following. a). The values for x for which f(x) = 0. b). The values for x for which g(x) = 0. c). The values for x such that f(x) = g(x). d). The values for x such that f(x) greaterthanorequalto g(x). e). The values for x such that g(x) greaterthanorequalto f(x). f). Estimate g(3 pi/4). g). f(3 pi/2) =

Solution

a) f(x) = 0 =====> x = 0, , 2

b) g(x) = 0 =====> x = /2, 3/2

c) f(x) = g(x) =======> /4, 5/4

d) f(x) >= g(x) =======> /2, 3/4,

e) g(x) >= f(x) =======> 0, 3/2, 7/4, 2

f) g(3/4) = cos(3/4) = -0.707

g) f(3/2) = sin(3/2) = 0