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Sin(42 o ) = 0.669130606 = 0.6691 ( 4 d.p._.
YES!!!! Sin(2x) = Sin(x+x') Sin(x+x') = SinxCosx' + CosxSinx' I have put a 'dash' on an 'x' only to show its position in the identity. Both x & x' carry the same value. Hence SinxCosx' + CosxSinx' = Sinx Cos x + Sinx'Cosx => 2SinxCosx
The expression (\sin(3\alpha)) can be expanded using the triple angle formula for sine, which is (\sin(3\alpha) = 3\sin(\alpha) - 4\sin^3(\alpha)). This formula allows you to express (\sin(3\alpha)) in terms of (\sin(\alpha)).
You can use the Pythagorean identity to solve this:(sin theta) squared + (cos theta) squared = 1.
cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25) Note: cos(a)=cos(-a) for any angle 'a'. cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.