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evaluate cos of 5pi/6?
without using calculator
1 Answer
- BramblyspamLv 71 decade agoFavorite Answer
A full circle has 360 degrees.
A full circle has 2pi radians.
Hence, 2pi radians = 360 degrees
So pi radians = 180 degrees
And (5/6)pi radians = (5/6)*180 degrees, or 150 degrees.
Remember the side length ratios of a 30-60-90 triangle? They're 1-(1/2)-(sqrt(3)/2).
Visualizing where the 150 degree (or 5/6 pi) triangle falls in the unit circle, it should be clear that the cosine of the angle is of length sqrt(3)/2, and has a negative sign.
The answer is thus -sqrt(3)/2.
Hope that helps!