What is the general solution for 3cos(3x)-15sin(3x)=0 ?

The general solution for 3cos(3x)-15sin(3x)=0 is x=(0.19739…)/3+(pin)/3

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3cos(3x)-15sin(3x)=0

3 cos (3 x) - 15 sin (3 x) = 0

x = \frac{0.19739 \dots}{3} + \frac{πn}{3}

Solution steps

3 cos (3 x) - 15 sin (3 x) = 0

Rewrite using trig identities

3 - 15 tan (3 x) = 0

Move

3

to the right side

- 15 tan (3 x) = - 3

Divide both sides by

- 15

tan (3 x) = \frac{1}{5}

Apply trig inverse properties

3 x = arctan (\frac{1}{5}) + πn

Solve

3 x = arctan (\frac{1}{5}) + πn : x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

x = \frac{arctan ( \frac{1}{5} )}{3} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{0.19739 \dots}{3} + \frac{πn}{3}

2 tan (x) - 3 cot (x) = 0

8 sin (2 x) + 15 cos (x) = 0

cos (\frac{x}{2}) - 2 cos (x) - 2 = 0

8 \cdot cos^{2} (3 x) + 6 \cdot cos (6 x) = 10216

sin (x) = \frac{48 \cdot sin ( 6 9 ^{\circ} )}{47.5}

What is the general solution for 3cos(3x)-15sin(3x)=0 ?
The general solution for 3cos(3x)-15sin(3x)=0 is x=(0.19739…)/3+(pin)/3