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

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

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Answer 1 · 2016-04-03T20:03:18

$1 - sqrt3 ≈ -0.732$

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

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

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

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

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