Question

Solve : Sin 2theta-cos3theta=0​

Answer 1

Answer:

theta = $\frac{\pi }{4}$ + 2$\pi$n, $\frac{3\pi }{4}$ + 2$\pi$n, $\frac{5\pi }{4}$ + 2$\pi$n, $\frac{7\pi }{4}$ + 2$\pi$n

Step-by-step explanation:

sin^2 theta - cos^3 theta = 1

cos^3 theta = 1 - sin^2 theta

sin^2 theta - cos^3 theta = 0

Substitute

sin^2 theta - ( 1 - sin^2 theta ) = 0

Distribute negative

sin^2 theta - 1 + sin^2 theta = 0

Combine same values

2sin^2 theta - 1 = 0

2sin^2 theta = 1

sin^2 theta = $\frac{1}{2}$

sin theta = +- $\frac{1}{\sqrt{2}}$

Right Triangle:  1 - 1 - $\sqrt{2}$

theta = $\frac{\pi }{4}$ + 2$\pi$n, $\frac{3\pi }{4}$ + 2$\pi$n, $\frac{5\pi }{4}$ + 2$\pi$n, $\frac{7\pi }{4}$ + 2$\pi$n

period of Sin function is 2$\pi$