Cos(450) = 1/(2)1/2 = 0.707
cos 315 degrees is 4th quadrant same as cos (-45) degrees which is +0.7071
1 cot(theta)=cos(theta)/sin(theta) cos(45 degrees)=sqrt(2)/2 AND sin(45 degrees)=sqrt(2)/2 cot(45 deg)=cos(45 deg)/sin(deg)=(sqrt(2)/2)/(sqrt(2)/2)=1
cos(495) = cos(495-360) = cos(135) = -cos(180-135) = -cos(45) = -sqrt(1/2) or -1/sqrt(2)
x = 45 degrees sin(x) = cos(x) = 1/2 sqrt(2)
Cos 43
cos 315 degrees is 4th quadrant same as cos (-45) degrees which is +0.7071
1 cot(theta)=cos(theta)/sin(theta) cos(45 degrees)=sqrt(2)/2 AND sin(45 degrees)=sqrt(2)/2 cot(45 deg)=cos(45 deg)/sin(deg)=(sqrt(2)/2)/(sqrt(2)/2)=1
It is 45 + 360*k deg or 135 + 360*k degrees where k is an integer.
Assuming that the angles are all stated in degrees: sin(45) = cos(45) = 1/2 sqrt(2) sin(45) cos(45) = (1/2)2 x (2) = 1/2 sin(230) = - 0.7660444 sin(45) cos(45) - sin(230) = 0.5 + 0.7660444 = 1.2660444 (rounded)
cos(45) = sin(45) You can see this as follows: imagine a circle with radius 1. The point on the circle with angle 45 degrees, lies on the line y=x, equally far from the x-axis (cos) as the y-axis (sin). The angle for both must be 45, because x and y are orthogonal: 90 deg, so if the angle with x is 45, then the angle with y must be 90-45=45. So: for this point, both angles are 45, and the distance to x (cos) is equal to the distance to y (sin). Therefore, cos(45) = sin(45). Additionally, cos(45) = sin(45+90) = sin(45+360n) = sin(135+360n) with n integer.
cos(495) = cos(495-360) = cos(135) = -cos(180-135) = -cos(45) = -sqrt(1/2) or -1/sqrt(2)
By shifting the sine wave by 45 degrees.
You must think of the unit circle. negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example: cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4
x = 45 degrees sin(x) = cos(x) = 1/2 sqrt(2)
sin(45) = cos(45) = 1/sqrt(2) tan(45) = cot(45)= 1 csc(45) = sec(45) = sqrt(2)
The cosine of 15 degrees can be calculated using the cosine subtraction formula: ( \cos(15^\circ) = \cos(45^\circ - 30^\circ) ). This gives us ( \cos(15^\circ) = \cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ ). Plugging in the known values, ( \cos 45^\circ = \frac{\sqrt{2}}{2} ), ( \cos 30^\circ = \frac{\sqrt{3}}{2} ), ( \sin 45^\circ = \frac{\sqrt{2}}{2} ), and ( \sin 30^\circ = \frac{1}{2} ), we find that ( \cos 15^\circ = \frac{\sqrt{6} + \sqrt{2}}{4} ).
The statement of the problem is equivalent to sin x = - cos x. This is true for x = 135 degrees and x = -45 degrees, and also for (135 + 180n) degrees, where n is any integer.