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.
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
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
You can use your trigonometric functions (sine, cosine, and tangent).
Sine is NOT the y coordinate: it is the sine of the angle made by the x-axis and the radius from a point on the circle. It is the cosine of the angle made with the y-axis.Consider any point, P, on the unit circle with coordinates (x, y). And let Q be the foot of the perpendicular from P to the x-axis. Then y = PQ.Now, in the right angled triangle OPQ, if OP makes an angle theta with the x axis, then sin(theta) = PQ/OP = y/OP and since OP is the radius of a unit circle, OP = 1 so that sin(theta) = y.
-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.
Cosine squared theta = 1 + Sine squared theta
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 (90- theta) = sine (theta)
That is not a question.
sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)
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.
Yes. (Theta in radians, and then approximately, not exactly.)