Question

How do you evaluate `2 sin (pi/6) - 3 tan (pi/6)`?

Answer 1

`1 - sqrt3 ≈ -0.732`

Explanation:

Using the `color(blue)" exact value triangle "`

For angles `pi/3 , pi/6 , pi/2`

with sides of length 1 ,`sqrt3" and hypotenuse " 2`

From this : `sin(pi/6) = 1/2" and " tan(pi/6) = 1/sqrt3`

hence `2sin(pi/6) = 2xx1/2 = 1`

and `3tan(pi/6) = 3xx1/sqrt3`

rationalising the denominator

`3xx1/sqrt3 = 3xxsqrt3/(sqrt3xxsqrt3) = (3sqrt3)/3 = sqrt3`

`rArr2sin(pi/6) - 3tan(pi/6) = 1 - sqrt3 ≈ -0.732`