using the sum or difference formula?

Question

I just checked my email and the instructor emailed saying to solve this problem before school. I have tried everything I could think of and I just can't get the problem to solve. Any suggestions?

cos (5pi/6)

I appreciate it.

Answer 1

cos(5pi/6) = cos(pi - pi/6)
cos(pi - pi/6) = cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
cos(pi - pi/6) = cos(pi)cos(pi/6) - sin(pi)sin(pi/6)
cos(pi - pi/6) = -(root3)/2 - 0
cos(pi - pi/6) = -(root3)/2

cos(5pi/6) = -(root3)/2

there u go, just remember the cos(a + b) formula.

Answer 2

cos (5pi/6) = cos(2pi/6 + 3pi/6) = cos(pi/3 + pi/2)
Now use the sum formula:
cos(pi/3 + pi/2) = cos(pi/3)cos(pi/2) - sin(pi/3)sin(pi/2)
= (1/2)(0) - (sqrt(3)/2)(1)
= - sqrt(3)/2

This is a pretty silly way to figure this out. You can also just know that 5pi/6 has a reference angle of pi/6, and it's in the second quadrant, where cosine is negative. So cos(5pi/6) = -cos(pi/6) = -sqrt(3)/2.

Answer 3

i do no longer kow the way you're breaking seventy 5 up. Trig SUM: cos (A + B)= cosA*cosB - sinA*sinB difference: cos (A - B) = cosA*cosB + sinA*sinB ex) sin 30 = a million/2, cos 30= ?3/2, sin 40 5 = cos 40 5= ?2/2 cos seventy 5 = cos(40 5 + 30) = cos 40 5 * cos 30 - sin 40 5 * sin 30 =?2/2 * ?3/2 - ?2/2 * a million/2 ? ?6/4 -?2/4 very final answer: (?6 - ?2)/4

Answer 4

cos (5pi/6) = cos 150 degrees = -.8660254036
Also, cos (5pi/6) = -sqrt(3)/2 for an exact answer.

Answer 5

cos (5pi/6)=
cos(pi-(pi/6)=
-cos(pi/6)=
-√3/2

Answer 6

cos (5π / 6) = - cos (π / 6) = - √3 / 2

Answer 7

And, after all that, do you know where the root3 over two comes from ?

Answer 8

It's equal to - 0.5*sqrt(3). What do you want to do with it?