If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
Yes. (Theta in radians, and then approximately, not exactly.)
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
If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432
Yes. (Theta in radians, and then approximately, not exactly.)
-1 < sine(theta) < 1 so sine(theta) cannot be 3125
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.
We'll answer your question as asked. What was asked was, "What is the sine of the angle (the angle theta) if the angle measures 0.4384?" That's the way the question reads. That's a pretty small angle. Less than one degree. That angle has about 0.00765 as the sine. Perhaps the question was "What is the angle of theta if its sine is 0.4384?" In the event that this was really your question, if sine theta equals 0.4384, arcsine theta is about 23.00 degrees. Here we use the term arcsine. If we see "arcsine 0.4384" in a text, what it means is "the angle whose sine is 0.4384" in math speak.
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)