FInd the exact values of cos150 and sin150
cos = -√3/2, sin = 1/2
cos -1/2, sin √3/2
cos 1/2, sin = 1/2
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.
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)
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.
To find the exact values of cos150 and sin150, we can use the properties of trigonometric functions and the values of cos30 and sin30.
We know that cos(180 - θ) = -cosθ and sin(180 - θ) = sinθ.
Since 150 = 180 - 30, we can use these properties to find the exact values of cos150 and sin150.
cos150 = -cos30 = -(√3/2) = -√3/2
sin150 = sin30 = 1/2
Therefore, the exact values of cos150 and sin150 are:
cos150 = -√3/2
sin150 = 1/2