Oh honey, cos 45 degrees is just 0.7071. It's like asking me what color the sky is - it's blue, duh. So, go ahead and plug that number into your trig functions and strut your stuff with that knowledge.
cos(195) = cos(180 + 15) = cos(180)*cos(15) - sin(180)*sin(15) = -1*cos(15) - 0*sim(15) = -cos(15) = -cos(60 - 45) = -[cos(60)*cos(45) + sin(60)*sin(45)] = -(1/2)*sqrt(2)/2 - sqrt(3)/2*sqrt(2)/2 = - 1/4*sqrt(2)*(1 + sqrt3) or -1/4*[sqrt(2) + sqrt(6)]
When the angle X = 45 or 225 degrees, or any other angle that falls at the same position as one of these angles in polar coordinates.
The question is somewhat ambiguous, but the answer is probably 45 degrees.
45 degrees. 360 degrees divided by 8 is 45.
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
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)
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
By shifting the sine wave by 45 degrees.
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 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.
Usually you can get the sine or cosine of an angle from a calculator very quickly. However, many calculators won't tell you that the result, which is about 0.707, is exactly 1 / square root of 2, or the equivalent square root of 2 / 2.
0.1333