1st-the reason i keep change my name because some of my friends are using my computer by their own name to asked questions. we are having a hard time solving each trig problems

2nd- if sin theta=0.6 and 90 degree <theta < 180 degree, find the exact value of sin 2 theta.
a.-0.6
b.-0.96
c.0.96
d. .28

sin theta=.6 >>> theta= arc sin .6=36.86or 90-36.86

sin106=.96

To find the exact value of sin 2 theta when sin theta is given, we can use the double angle formula for sine. The formula states that sin 2 theta = 2 * sin theta * cos theta.

Given that sin theta is 0.6 and 90 degrees < theta < 180 degrees, we can determine the value of cos theta using the Pythagorean identity: sin^2 theta + cos^2 theta = 1.

Since sin theta is given as 0.6, we can solve for cos theta as follows:

sin^2 theta + cos^2 theta = 1
0.6^2 + cos^2 theta = 1
0.36 + cos^2 theta = 1
cos^2 theta = 1 - 0.36
cos^2 theta = 0.64
cos theta = √0.64
cos theta = 0.8

Now that we have the values of sin theta and cos theta, we can substitute them into the double angle formula to find sin 2 theta:

sin 2 theta = 2 * sin theta * cos theta
sin 2 theta = 2 * 0.6 * 0.8
sin 2 theta = 0.96

Therefore, the exact value of sin 2 theta is 0.96. The correct answer is c.