Question

On which interval is y = sin(x) strictly increasing?

(Negative pi, negative StartFraction pi Over 2 EndFraction)

(0, pi)

(StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 2 EndFraction)

(0, StartFraction pi Over 2 EndFraction)

Answer 1

D. (0, pi/2)

Explanation:

If you graph y=sin(X) (I used desmos) then you find that the graph is increasing from 0 to pi/2 :)

Answer 2

The function is strictly increasing on (0, π/2)

Explanation:

We are given the function;

y = sin x

Let's find the derivative;

dy/dx = cos x

Now, Cos 0 = 1

Cos (π/4) = 1/√2

Cos (π/2) = 0

From the above, we can see that as x approaches 0 from (π/2), the value of (cos x) approaches 1. This means it's increasing from 0 to 1.

Thus, the function is strictly increasing on the interval (0, π/2)