Question

How do you find the value of `cos(pi/3 - pi/6)`?

Answer 1

`1/2 sqrt3`

Explanation:

Using the appropriate `color(blue)" Addition formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos(A +- B)= cosAcosB ∓ sinAsinB )color(white)(a/a)|)))`

`rArr cos(pi/3 - pi/6) = cos(pi/3)cos(pi/6) + sin(pi/3)sin(pi/6)`

Now using the `color(blue)" exact value triangle "`

with angles of `pi/6 , pi/3 , pi/2" and sides " 1 , 2 , sqrt3 " we obtain "`

`cos(pi/3) = 1/2 , cos(pi/6) = (sqrt3)/2`

and `sin(pi/3) = (sqrt3)/2 , sin(pi/6) = 1/2`

substituting these values into the right side of the expansion.

`= [1/2xx(sqrt3)/2] +[ (sqrt3)/2xx 1/2] = 1/4 sqrt3 + 1/4 sqrt3 = 1/2 sqrt3`

Answer 2

I would do the subtraction first.

Explanation:

`cos(pi/3-pi/6) = cos((2pi)/6-pi/6) = cos(pi/6) = sqrt3/2`