Question

What is the exact value of (cos(195^∘))?

A. -√6-√2/4
B. √6-√2/4
C. (√6+√2)/4
D. -(√2+√6)/4

Answer 1

To find the exact value of cos(195°), we can use the unit circle. The correct answer is -√6-√2/4.

Step-by-step explanation:

To find the exact value of cos(195°), we can use the unit circle. In the unit circle, the angle 195° is in the third quadrant, where cosine is negative. Therefore, cos(195°) is a negative value. Let's find the value:

Start by finding the reference angle: 195° - 180° = 15°

In the third quadrant, cosine is negative. So, cos(195°) = -cos(15°)

Now, let's find the exact value of cos(15°). We can use the half angle formula to simplify it: cos(15°) = sqrt((1 + cos(30°)) / 2)

Using the value of cos(30°) = sqrt(3) / 2, we can simplify it further:cos(15°) = sqrt((1 + sqrt(3) / 2) / 2)

This simplifies to: cos(195°) = -sqrt(6) - sqrt(2) / 4. So, the correct answer is option A.