Determine the exact value of cos 465 degrees

a) √3 + √2/2

b) √2 + √3√2/4

c)√2 - √3√2/4

d)2+√2-√3√2/4

To determine the exact value of cos 465 degrees, we can use the unit circle or trigonometric identities.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. The angles formed with the positive x-axis are measured in degrees or radians. The values of trigonometric functions (such as sine, cosine, and tangent) for angles on the unit circle can be determined.

To find the exact value of cos 465 degrees using the unit circle, we need to convert the angle to its equivalent within the range of 0 to 360 degrees. Since the cosine function has a periodicity of 360 degrees, we can subtract multiples of 360 from the angle until we get within this range.

465 degrees - 360 degrees = 105 degrees

Now that we have 105 degrees, we can use the unit circle to find the cosine value. In the first quadrant (0 to 90 degrees), the cosine value is positive.

Looking at the unit circle, we find that the reference angle for 105 degrees is 75 degrees. The cosine value for 75 degrees is √3 + √2/2.

Therefore, the correct answer is:

a) √3 + √2/2