This is a fairly straightforward trigonometry problem.
I'll assume you were give tan(θ)=(-1) for 0o < θ < 360o in this situation.
I strongly suggest you familiarize yourself with the unit circle. In this case, we are looking for a point on the circle where the slope between (0,0) and the point at θ is (-1). This occurs at 135o and 315o.
Short Answer: θ = {135o, 315o}
Sin (theta + 180) is equal to -sin (theta) because the sin function is symmetrically opposite every 180 degrees. Proof: Draw a unit circle, radius 1, centered at the origin (x=0, y=0). Pick any point on that circle, and draw a line from that point through the origin and to the opposite edge of the circle. The angle between that line and the x-axis going to the right is theta. It ranges from 0 degrees at (x=1, y=0) to 360 degrees coming back to (x=1, y=0) rotating counter-clockwise. (The angle is called theta to avoid confusion with the question's original use of x.) The x and y coordinates of the first point are symmetrically opposite the x and y coordinates of the second point. (If X1 were 0.35, for instance, then X2 would be -0.35.) The same goes for Y. (There are two right triangles, with the hypotenuses equal and two angles equal; therefore the two triangles are the same, just flipped over.) Sin (theta) in a unit circle is defined in trigonometry as y, so sin (theta + 180) is equal to -y, which is the same as -sin (theta). Sin (theta) is actually y divided by hypotenuse or "opposite over hypotenuse" but, since the hypotenuse is 1, that can be ignored - it does not change the answer.
360 - 301 = 59
Essentially, none. Every negative angle can be made positive by adding 2*pi radians (or 360 degrees, or a multiple).
Because it is an quadrilaterial with four equal sides that sum up to 360
0 ================================== Another contributor says: Yes, x=0 is a solution, but there are a lot more. sin(2x) = sin(x) whenever x = (N pi) radians or x = (2N-1) pi / 3 radians. 1 radian = 57.3 degrees (rounded) Make ' N ' any whole number you want. The first cycle of angles are: X = pi/3, pi, 5 pi/3, 2 pi radians or 60, 180, 300, 360 degrees.
108.435 degrees 288.435 degrees (decimal is rounded)
- cos theta
The answer is 60 and 240 degrees. Add radical 3 and inverse tan to get answer add 180 for other answer less than 360.
4 sin(theta) = 2 => sin(theta) = 2/4 = 0.5. Therefore theta = 30 + k*360 degrees or 150 + k*360 degrees where k is any integer.
-0.5736
They are 35.1 and 324.9 degrees.
2 sin (Θ) + 1 = 0sin (Θ) = -1/2Θ = 210°Θ = 330°
No, not necessarily. Cosine theta is equal to 1 only when theta is equal to zero and multiples of 2 pi radians or multiples of 360 degrees. This is because cosine theta is hypotenuse over adjacent, and the ratio 1 only occurs at 0, 360, 720, etc. or 0, 2 pi, 4 pi, etc.
cos(theta) = 0.7902 arcos(0.7902) = theta = 38 degrees you find complimentary angles
Given that theta is the angle with respect to the positive X axis of a line of length 1, then sin(theta) = Y and cos(theta) is X, with (X,Y) being the point at the end of the line. As theta sweeps from 0 to 360 degrees, or 0 to 2 pi radians, that point draws a circle of radius 1, with center at (0,0).Since X, Y, and 1 form the sides of a right triangle, where 1 is the hypotenuse, then the pythagorean theorem states that X2 + Y2 = 12. This means that sin2(theta) + cos2(theta) = 1.Tan(theta) is defined as sin(theta) divided by cos(theta), or Y / X. Since division by zero is a limiting invalidity, then tan(theta) is asymptotic to Y=0, having value of +infinity at theta = 90 or pi / 4, and -infinity at 270 or 3 pi / 4.
Each angle theta is (n-2)/n) x 180 degrees The sum of all angles is nx theta = (n-2) x 180 sum = 180 n - 360 sum + 360 = 180 n n = (sum + 360)/180 = sum/180 + 2 So you divide sum by 180 then add 2
For angles between 90 and 180 use the angle (180 - X) For angles between 180 and 270 use (X - 180) For angles between 270 and 360 use (360 - X) For angles greater than 360 subtract 360 until the angle is between 0 and 360 degrees and one of the above rules can be applied. You need to be careful with the signs of the ratios.