sin-1 (0.91) = about 1.14328 radians.
Cosine squared theta = 1 + Sine squared theta
2
The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X. The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.
0.75
No, they cannot all be negative and retain the same value for theta, as is shown with the four quadrants and their trigonemtric properties. For example, in the first quadrant (0
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.
That depends on the value of the angle, theta. csc is short for "cosecans", and is the reciprocal of the sine. That is, csc theta = 1 / sin theta.
The answer will depend on where, in the sine function, the x-value appears: For example, its roles in f(x) = sin(x), or f(x, theta) = x*sin(theta) or f(x, theta) = sin(x*theta) f(theta) = sin(theta + x) are quite different.
-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.
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
Cosine squared theta = 1 + Sine squared theta
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.
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)