(3) DeMoivre's formula is another consequence of the polar form of a complex number, it states: (cos 0+i sin 0)" cos no + i sin no. %3D (a) Re-derive the double angle formulas for sine and cosine using DeMoivre's formula. (b) Find triple angle formulas for sine and cosine.

Converting complex numbers from polar form to rectangular form. Use exact values for trigonometric functions, for example, tan 30° enter as 1/sqrt(3)). = b √3 (which one would Convert the complex number z = 10e225°i. to rectangular form z = a + bi

Use the Pythagorean Identity to write the double angle formula for cosine in two alternate forms by filling in the blanks using a trig identity or simplifying your answer at each step. (a) cos(2t)=1−2sin2(t)=1−(cos⁡(2t)=1−2sin2⁡(t)=1−(  )=)=  help (formulas) (b) cos(2t)=2cos2(t)−1=2cos2(t)−(cos⁡(2t)=2cos2⁡(t)−1=2cos2⁡(t)−(  )=)=  help (formulas)

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