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.
sin-1(0.707) = 44.99134834 or about 45 degrees
If sin(theta) is 0.9, then theta is about 64 degrees or about 116 degrees.
sin(90) = 1
sin(360+30) =sin(30)= 1/2
They are both trig values, but not equal. Tan 45 is 1 and sin 45 is 0.7071
This problem can be solved using the Sine Rule :a/sin A = b/sin B = c/sin C 10/sin 45 = AB/sin 75 : AB = 10sin 75 ÷ sin 45 = 13.66 units (2dp)
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.
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
sin-1(0.707) = 44.99134834 or about 45 degrees
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.
sin 57 degrees
x = 45 degrees sin(x) = cos(x) = 1/2 sqrt(2)
No; those could be three different values, or sometimes two of them might be the same. For example, if the angle is 45 degrees, the values are about... cos:0.707 sin: 0.707 tan: 1 For 45 degrees, the cosine and sine are the same. For 36 degrees, cos:0.809 sin: 0.588 tan: .727
45 degrees North-------------------------------The answer "45 degrees North" is incorrect. Since the Earth is an oblate ellipsoid, the actual halfway point lies 16.0385 km north of the 45th parallel. As best I can calculate, based on the WGS84 ellipsoid, this parallel is 45 degrees, 8 minutes, 39.544 seconds North latitude, or 45.14432 degrees North.45 degrees North lies 4,984.944 km from the Equator, or only 49.84% of the 10,001.966 km to the North Pole. The point specified above lies exactly halfway at 5,000.983 km away.My estimate is based on the Delambre series for the WGS84 ellipsoid, using the formula m(φ) = 6367449.146φ − 16038.509 sin 2φ + 16.833 sin 4φ − 0.022 sin 6φ + 0.00003 sin 8φ where m(φ) is the distance from the equator and φ is the latitude.(Source: wikipedia)