What is the cosine of Pi/6?

Question

I don't have a graphing calculator where I am at right now

Answer 1

cos π/6 =

π/6(180/π) =

π cancells

6 divided into 180 = 30°

cos 30° = 0.866025404

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Answer 2

Two useful triangles are:
the equilateral 1 x 1 x 1
and the rt angle isosceles 1 x 1 x sqrt(2)

The latter gives an easy way of calculating sin, cos, and tan of 45 degrees (pi/4)
sin and cos are both 1/sqrt(2) written more commonly as sqrt(2)/2
tan (pi/4) = 1/1 = 1

In the equilateral triangle, above, drop a perpendicular from one of the vertices to the other side, creating two congruent 30/60/90 degree triangles.

These triangles have hypotenuse as 1 unit, and the leg opp the 30 degrees is half a side = 1/2 unit.
The side opp the 60 degrees is hence:
sqrt(1^2 - (1/2)^2) = sqrt(3/4) = sqrt(3)/2

This gives us an easy way of calculating sin, cos, and tan of both pi/3 (60 degrees) and pi/6 because the sides opp the 30/60/90 are known:
1/2, sqrt(3)/2, and 1 unit

For your case,
cos(pi/6) = (sqrt(3)/2 )/1 = sqrt(3)/2

Answer 3

You don't need a graphing calculator for this one. Pi/6 is just a 30 degree angle. Cos (30 deg) = sqrt(3)/2 = 0.866

Answer 4

But you seem to have access to a computer.

If it has Excel, open up a worksheet. For any square, enter the formula:
=COS(PI()/6)
(Excel works in radians)

To get the value for pi, you must always put an empty set of brackets right after, like pi()

If you want the tangent of 3Pi/4, then
=TAN(3*PI()/4)
or
=TAN(0.75*PI())
note the two closing brackets at the end, one for PI() and one to close the value of the angle.

Answer 5

pi/6 is thirty degrees. the cosing of 30 degrees is .866 approx

Answer 6

root 2 over 2

Answer 7

0.866025 = sqrt(3)/2