inverse cos (-rad2/2)=135 degrees
inverse sin (-rad2/2)=-45 degrees
I don't understand why cos is 135
for the cosine = -sqrt 2/2 negative x axis
means quadrant 2 or quadrant 3
It could be either 180 + 45 or 180 - 45
so either 135 or 225
for the sine = -sqrt 2/2
means quadrant 3 or quadrant 4
that is 180 + 45 or 360 - 45
so either 225 or 315
225 satisfies both the sine and the cosine.
To understand why inverse cosine of (-√2/2) is 135 degrees, you need to first understand what the inverse cosine function means.
The inverse cosine function (also known as arccosine or cos^-1) returns the angle whose cosine is equal to a given value. In other words, it tells you the angle that produces a specific cosine value.
For the value (-√2/2), we can use the unit circle to find the angle. The unit circle is a circle with a radius of 1 centered at the origin (0,0) in a coordinate plane.
To find the angle that has a cosine of (-√2/2), we look for the x-coordinate on the unit circle that matches this value. We know that cosine is equal to the x-coordinate on the unit circle.
In this case, the value (-√2/2) corresponds to the point on the unit circle where x = -√2/2. Using the unit circle, this occurs at an angle of 135 degrees.
So, the inverse cosine of (-√2/2) is equal to 135 degrees.