Question

[ cos(0) = √2/2 and 3pi < 0 < 2pi, ] evaluate (sin(0)) and (tan(0)).

A. (sin(0) = √2/2), (tan(0) = 1)
B. (sin(0) = -√2/2), (tan(0) = -1)
C. (sin(0) = √2/2), (tan(0) = -1)
D. (sin(0) = -√2/2), (tan(0) = 1)

Answer 1

To evaluate sin(0) and tan(0), we can substitute the given value of cos(0) into the equations. sin(0) = 1/2 and tan(0) = sqrt(2)/2.

Step-by-step explanation:

To evaluate sin(0) and tan(0), we can use the values of cos(0) = sqrt(2)/2 and 3pi < 0 < 2pi. Since sin(x) = sqrt(1 - cos^2(x)) and tan(x) = sin(x)/cos(x), we can substitute the given value of cos(0) into the equations to find the values of sin(0) and tan(0).

sin(0) = sqrt(1 - (sqrt(2)/2)^2) = sqrt(1 - 2/4) = sqrt(1/4) = sqrt(1)/sqrt(4) = 1/2

tan(0) = sin(0)/cos(0) = (1/2) / (sqrt(2)/2) = (1/2) * (2/sqrt(2)) = 1/sqrt(2) = sqrt(2)/2 = 0.7071