give the value of each expression in simplest radical form of sine -45 deprees
To find the value of the expression sine (-45 degrees) in simplest radical form, we need to use the unit circle and the concept of special angles.
First, let's recall the unit circle, which is a circle with a radius of 1 unit, centered at the origin (0, 0) of a coordinate plane. In the unit circle, the angle is measured in counterclockwise direction from the positive x-axis.
Now, let's find the value of sine (-45 degrees) using the unit circle. Since the angle is negative, we can determine the equivalent positive angle by adding 360 degrees to it, i.e., (-45 + 360 = 315 degrees).
Next, we look for the angle 315 degrees on the unit circle. This angle is in the fourth quadrant. In the fourth quadrant, sine is negative. Therefore, we need to find the negative value of sine at 315 degrees.
On the unit circle, the coordinates of the point corresponding to 315 degrees are (1/√2, -1/√2). This means that the sine of 315 degrees is -1/√2.
Hence, the value of the expression sine (-45 degrees) in simplest radical form is -1/√2.