Find the exact value of cos 315 degrees.
answers: 3/2, -1/2,2/2, -2/2
To find the exact value of cos 315 degrees, we will use the unit circle.
First, let's determine which quadrant 315 degrees falls in. In the unit circle, 0 degrees is at the positive x-axis and we move counterclockwise from there.
315 degrees is in the fourth quadrant as it goes three-quarters of the way around the circle from 0 degrees.
In the fourth quadrant, the x-coordinate (cosine) is positive.
Since cos 315 degrees is positive, the exact value of cos 315 degrees is + (√2 / 2).
Therefore, the answer is √2 / 2 or approximately 0.707.
To find the exact value of cos 315 degrees, we can use the special angles and the unit circle. Recall that the unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane.
In the unit circle, we can draw an angle of 315 degrees, which lies in the fourth quadrant. To find the cosine of this angle, we can use the fact that cosine is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.
In the fourth quadrant, the x-coordinate is negative and the y-coordinate is negative. So, the point that corresponds to an angle of 315 degrees in the unit circle is (-√2/2, -√2/2).
Therefore, cos 315 degrees is equal to -√2/2, which can also be written as -1/√2 or -√2/2.
Therefore, the correct answer is -√2/2.
315 ° = 360 ° - 45 °
cos ( 360 ° - theta ) = cos ( theta )
cos ( 360 ° - 45 °) = cos ( 45 ° ) = square root ( 2 ) / 2