FInd the exact values of cos150 and sin150

Question

cos = -√3/2, sin = 1/2
cos -1/2, sin √3/2
cos 1/2, sin = 1/2

Answer 1

Using the unit circle, we see that 150 degrees is in the second quadrant, which means cos150 is negative and sin150 is positive.

To find cos150, we can use the cosine formula for 180 minus an angle: cos(180 - θ) = -cosθ. So, we have:

cos150 = -cos(180 - 150) = -cos30 = -√3/2

To find sin150, we can use the sine formula for 180 minus an angle: sin(180 - θ) = sinθ. So, we have:

sin150 = sin(180 - 150) = sin30 = 1/2

Therefore, cos150 = -√3/2 and sin150 = 1/2.

Answer 2

Note: Enter your answer and show all the steps you use to solve this problem in the space provided.
Multiply and simplify if possible.
(6-√3) (4+√3)

Answer 3

To expand the expression, we need to distribute each term in the first parenthesis to every term in the second parenthesis:

(6 - √3) (4 + √3) = 6(4) + 6(√3) - √3(4) - √3(√3)

Now we simplify by multiplying and combining like terms:

= 24 + 6√3 - 4√3 - 3
= 21 + 2√3

Therefore, (6 - √3) (4 + √3) simplifies to 21 + 2√3.