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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.
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What is sin 45?
one over the square root of 2 or 0.850903525
What is sin 45 degrees?
1/square root 2
What if the sine of an angle is 0.707 what is value of that angle in degrees?
sin-1(0.707) = 44.99134834 or about 45 degrees
When is the shadow equal in length to your height?
When the angle of elevation equals 45 degrees. tan-1(1) = 45 degrees.
What is the cos of a 45 degree angle?
cos 45o = 1/√2 = 1/2 x √2 ≈ 0.707
