What is sin^3(x+(3pi)/2) ?

The solution to sin^3(x+(3pi)/2) is -cos^3(x)

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simplify sin^3(x+(3pi)/2)

simplify

sin^{3} (x + \frac{3 π}{2})

- cos^{3} (x)

Solution steps

sin^{3} (x + \frac{3 π}{2})

Rewrite using trig identities

= (- cos (x))^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- cos (x))^{3} = - cos^{3} (x)

= - cos^{3} (x)

cos (x) + cos (x - \frac{π}{3})

- sin (p i t - 4 p i t)

tan (π - 3 x)

2 sin (2 x + 1 5^{\circ})

2 \cdot sin (2 x + \frac{π}{2})