What is the value of sin(20)+sin(40)+sin(80) ?

The value of sin(20)+sin(40)+sin(80) is 1.96961…

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sin(20)+sin(40)+sin(80)

sin (2 0^{\circ}) + sin (4 0^{\circ}) + sin (8 0^{\circ})

1.96961 \dots

Solution steps

sin (2 0^{\circ}) + sin (4 0^{\circ}) + sin (8 0^{\circ})

Refine to a decimal form

= 1.96961 \dots

200 (e^{- 2 π} cos (2))

sin (\frac{π}{2} + \frac{3 π}{4})

200 (e^{- 2 π} cos (2) + e^{- 4 π} cos (4))

\frac{sin ( 5 0 ^{\circ} )}{sin ( 1 0 ^{\circ} )} - 2 cos (4 0^{\circ}) - 2 cos (2 0^{\circ})

4 sin (- 1 5^{\circ})

What is the value of sin(20)+sin(40)+sin(80) ?
The value of sin(20)+sin(40)+sin(80) is 1.96961…