What is sin(arccos(3x)) ?

The solution to sin(arccos(3x)) is sqrt(1-9x^2)

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simplify sin(arccos(3x))

simplify

sin (arccos (3 x))

1 - 9 x^{2}

Solution steps

sin (arccos (3 x))

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

= 1 - (3 x)^{2}

Simplify

= 1 - 9 x^{2}

4 - (2 sin (θ))^{2}

sin (arctan (\frac{x}{y}))

sin (36 0^{\circ} + x)

sin (x + 3 0^{\circ})

tan (9 0^{\circ} - a)