What is the general solution for 0=(6cos(30t)+2sin(30t)) ?

The general solution for 0=(6cos(30t)+2sin(30t)) is t=-(1.24904…)/(30)+(pin)/(30)

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0=(6cos(30t)+2sin(30t))

0 = (6 cos (30 t) + 2 sin (30 t))

t = - \frac{1.24904 \dots}{30} + \frac{πn}{30}

Solution steps

0 = (6 cos (30 t) + 2 sin (30 t))

Switch sides

(6 cos (30 t) + 2 sin (30 t)) = 0

Rewrite using trig identities

6 + 2 tan (30 t) = 0

Move

6

to the right side

2 tan (30 t) = - 6

Divide both sides by

2

tan (30 t) = - 3

Apply trig inverse properties

30 t = arctan (- 3) + πn

Solve

30 t = arctan (- 3) + πn : t = - \frac{arctan ( 3 )}{30} + \frac{πn}{30}

t = - \frac{arctan ( 3 )}{30} + \frac{πn}{30}

Show solutions in decimal form

t = - \frac{1.24904 \dots}{30} + \frac{πn}{30}

- 2 sin (θ) = 2

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

sin^{2} (\frac{x}{2}) - 1 = 0

69 = cos (x)

sin^{2} (θ) = cos (θ) + cos^{2} (θ)

What is the general solution for 0=(6cos(30t)+2sin(30t)) ?
The general solution for 0=(6cos(30t)+2sin(30t)) is t=-(1.24904…)/(30)+(pin)/(30)