Question

How do I find the value of sin 330?

Answer 1

`-1/2`

Explanation:

We know from trigonometry that

`sin(A-B)=sinA*cosB-cosA*sinB`

Hence

`sin330=sin(360-30)=sin360*cos30-cos360*sin30=0*sqrt3/2-1*1/2=-1/2`

Answer 2

The way I solve this is incorporating a myriad of different trigonometrical aspects into one solution.

Explanation:

First, we know that `sin 330` will be in the 4th quadrant, as it lies between `270` and `360` degrees.

Second, we know that when we add or subtract degrees from x in `sin x, cos x`, and `tan x` from 360 and 180, the trigonometric ratios stay the same, however, if we add/subtract degrees from x from `90` or `270` degrees, we turn the ratio to it's opposite: sin becomes cos, cos becomes sin, tan becomes cot.

Third, we know that only cos is positive in the 4th quadrant. This means that sin is negative.

The easiest way to go about doing this (with the least work possible) is to subtract a sin value from 360 degrees (as to not have to switch the trigonometric ratio being used).

360 - 330 = 30, so we are subtracting 30 degrees from 360 to get the sin inverse, 330.

Since we are subtracting from 360, the ratio will remain sin, and because it is in the 4th quadrant, the sin will be negative.

Therefore, our answer is `-sin(30)`, or `-1/2`

Sorry if this seems confusing, this is how I learnt it.