If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
For such simplifications, it is usually convenient to convert any trigonometric function that is not sine or cosine, into sine or cosine. In this case, you have: sin theta / sec theta = sin theta / (1/cos theta) = sin theta cos theta.
sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)
near zero
Yes. (Theta in radians, and then approximately, not exactly.)
-1 < sine(theta) < 1 so sine(theta) cannot be 3125
If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
For such simplifications, it is usually convenient to convert any trigonometric function that is not sine or cosine, into sine or cosine. In this case, you have: sin theta / sec theta = sin theta / (1/cos theta) = sin theta cos theta.
Your question is insufficiently precise, but I'll try to answer anyway. "Sine squared theta" usually means "the value of the sine of theta, quantity squared". "Sine theta squared" usually means "the value of the sine of the quantity theta*theta". The two are not at all the same.
Theta is just a Greek letter used to denote measurement of angle. Sine is a trigonometric function, i.e., the ratio of the side opposite to the angle theta to the hypotenuse of the triangle. So Sine theta means the value of sine function for angle theta, where theta is any angle.
Cosine squared theta = 1 + Sine squared theta
The sine theta of an angle (in a right triangle) is the side opposite of the angle divided by the hypotenuse.
cosine (90- theta) = sine (theta)
That is not a question.
sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)
near zero
The sine of an angle theta that is part of a right triangle, not the right angle, is the opposite side divided by the hypotenuse. As a result, you could determine the hypotenuse by dividing the opposite side by the sine (theta)...sine (theta) = opposite/hypotenusehypotenuse = opposite/sine (theta)...Except that this won't work when sine (theta) is zero, which it is when theta is a multiple of pi. In this case, of course, the right triangle degrades to a straight line, and the hypotenuse, so to speak, is the same as the adjacent side.