Question

What is the exact value of cos(5π/6)?

−√3/2

−1/2

√3/2

1/2

Answer 1

The exact value of cos(5π/6) is -1/2.

Step-by-step explanation:

The exact value of cos(5π/6) is -1/2.

To find the exact value of cos(5π/6), we can use the unit circle. In the unit circle, the x-coordinate represents the cosine of an angle. Since 5π/6 is in the second quadrant of the unit circle, the value of cos(5π/6) is negative. Moving counterclockwise from the positive x-axis, the closest angle in the second quadrant is π/6. The cosine of π/6 is 1/2, so cos(5π/6) is -1/2.

Answer 2

3rd option

Step-by-step explanation:

cos(
`(5\pi )/(6)` ) ← is an angle in the 2nd quadrant where cos < 0

= - cos(π -
`(5\pi )/(6)` )

= - cos(
`(\pi )/(6)` )

= -
`(√(3) )/(2)`