If cosa = 3/5 and a ∈ (0,90), what is sin2a?

Step-by-step explanation:

Given

cosA = =

Then the opposite side using Pythagorean triple is 4, thus

sinA =

Using the trigonometric identity

sin2A = 2 sinAcosA, then

sin2A = 2 × ×

         = =

Step-by-step explanation:

Double angle identity for sine is

.

We know . We now need to find to find our answer.

Recall the following :

.

Replace with :

Subtract on both sides:

Now to finally get the value of take the square of both sides:

Since is in the interval , then .

So let's finally find the numerical value of .

Side note:

If is between 0 and 90 degrees, then we are in the first quadrant.

If we are in the first quadrant, both and are positive.

77

step-by-step explanation: