What is the general solution for 2sin(t)+cos(2t)=0 ?

The general solution for 2sin(t)+cos(2t)=0 is t=-0.37473…+2pin,t=pi+0.37473…+2pin

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2sin(t)+cos(2t)=0

2 sin (t) + cos (2 t) = 0

t = - 0.37473 \dots + 2 πn, t = π + 0.37473 \dots + 2 πn

Solution steps

2 sin (t) + cos (2 t) = 0

Rewrite using trig identities

1 + 2 sin (t) - 2 sin^{2} (t) = 0

Solve by substitution

sin (t) = - \frac{- 1 + 3}{2}, sin (t) = \frac{1 + 3}{2}

sin (t) = - \frac{- 1 + 3}{2} : t = arcsin (- \frac{- 1 + 3}{2}) + 2 πn, t = π + arcsin (\frac{- 1 + 3}{2}) + 2 πn

sin (t) = \frac{1 + 3}{2} :

No Solution

Combine all the solutions

t = arcsin (- \frac{- 1 + 3}{2}) + 2 πn, t = π + arcsin (\frac{- 1 + 3}{2}) + 2 πn

Show solutions in decimal form

t = - 0.37473 \dots + 2 πn, t = π + 0.37473 \dots + 2 πn

2 cos^{2} (x) - 1 + cos (x) = 2

23 = csc (x) cot (x)

4 sin^{2} (x) - 4 sin (x) = - 1

sin^{2} (θ) = 3 cos^{2} (θ)

20 sin^{2} (x) + 27 cos (x) = 6

What is the general solution for 2sin(t)+cos(2t)=0 ?
The general solution for 2sin(t)+cos(2t)=0 is t=-0.37473…+2pin,t=pi+0.37473…+2pin