What is the general solution for 6cos(6t)+24sin(6t)=0 ?

The general solution for 6cos(6t)+24sin(6t)=0 is t=-(0.24497…)/6+(pin)/6

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6cos(6t)+24sin(6t)=0

6 cos (6 t) + 24 sin (6 t) = 0

t = - \frac{0.24497 \dots}{6} + \frac{πn}{6}

Solution steps

6 cos (6 t) + 24 sin (6 t) = 0

Rewrite using trig identities

6 + 24 tan (6 t) = 0

Move

6

to the right side

24 tan (6 t) = - 6

Divide both sides by

24

tan (6 t) = - \frac{1}{4}

Apply trig inverse properties

6 t = arctan (- \frac{1}{4}) + πn

Solve

6 t = arctan (- \frac{1}{4}) + πn : t = - \frac{arctan ( \frac{1}{4} )}{6} + \frac{πn}{6}

t = - \frac{arctan ( \frac{1}{4} )}{6} + \frac{πn}{6}

Show solutions in decimal form

t = - \frac{0.24497 \dots}{6} + \frac{πn}{6}

sin (x) = \frac{50 \cdot sin ( 14 5 ^{\circ} )}{120}

cos^{2} (θ) - cos (θ) = sin^{2} (θ)

sin (x) + 2 sin^{2} (x) = 0

5 sec^{2} (x) - 5 = 0, 0 \leq x \leq 2 π

4 cos^{2} (θ) + 4 = 5

What is the general solution for 6cos(6t)+24sin(6t)=0 ?
The general solution for 6cos(6t)+24sin(6t)=0 is t=-(0.24497…)/6+(pin)/6