Question

how to convert sin65.37?
​

Answer 1

as we know that trigonometric values of some functions i.e Sin(60) = √3 /2 = 0.87 sin(75) = (√3 +1 )/2√2 = 0.96 So approximate value of sin 65.37 lies between 0.87 and 0.

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Answer 2

sin(3)=3sin−4sin3cos(3)=cos3−3cossin2=cos3−3cos(1−cos2)
sin
⁡
(
3. Pls mark as
x
)
=
3
sin
⁡
x
−
4
sin
3
⁡
x
cos
⁡
(
3
x
)
=
cos
3
⁡
x
−
3
cos
⁡
x
sin
2
⁡
x
=
cos
3
⁡
x
−
3
cos
⁡
x
(
1
−
cos
2
⁡
x
)
Since you know sin(60)=3‾√/2
sin
⁡
(
60
)
=
3
/
2
, you know that the sine of 20 -- call it
u
-- satisfies the equation

3‾√/2=3−43
3
/
2
=
3
u
−
4
u
3
From this, you can solve for
u
(using Cardano's formula for the solution of a cubic). To be honest, this is a complete pain in the neck, but at least it's a route to the solution.