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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.

Q: What is the equivalent of sine theta over secant theta?

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There is none because it is not true.

If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432

sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)

near zero

It is the reciprocal of the sine ratio.

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In trigonometry, the value of R is the radius of the circle, and is usually normalized to a value of 1. If the circle is at the X-Y origin, and theta is the angle between the radius line R, and X and Y are the X and Y coordinates of the point on the circle at the radius line, then... sine(theta) = Y / R cosine(theta) = X / R secant(theta) = 1 / cosine(theta) = R / X cosecant(theta) = 1 / sine(theta) = R / Y

When you subtract theta from 180 ( if theta is between 90 degrees and 180 degrees) you will get the reference angle of theta; the results of sine theta and sine of its reference angle will be the same and only the sign will be different depends on which quadrant the angle is located. Ex. 150 degrees' reference angle will be 30 degrees (180-150) sin150=1/2 (2nd quadrant); sin30=1/2 (1st quadrant) 1st quadrant: all trig functions are positive 2nd: sine and csc are positive 3rd: tangent and cot are positive 4th: cosine and secant are positive

There is none because it is not true.

-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

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.

You don't have buttons for cotangent, secant, and cosecant because you don't need them. Just invert. Cotangent is 1 over tangent, secant is 1 over sine, and cosecant is 1 over cosine.

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

By converting cosecants and secants to the equivalent sine and cosine functions. For example, csc theta is the same as 1 / sin thetha.

Sine and cosine are cofunctions, which means that their angles are complementary. Consequently, sin (90° - x) = cos x. Secant is the reciprocal of cosine so that sec x = 1/(cos x). Knowing these properties of trigonometric functions, among others, will really help you in other advance math courses.

The sine theta of an angle (in a right triangle) is the side opposite of the angle divided by the hypotenuse.