What is the general solution for 2sin(30+x)=3cos(x) ?

The general solution for 2sin(30+x)=3cos(x) is x=0.85707…+180n

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2sin(30+x)=3cos(x)

2 sin (3 0^{\circ} + x) = 3 cos (x)

x = 0.85707 \dots + 18 0^{\circ} n

Solution steps

2 sin (3 0^{\circ} + x) = 3 cos (x)

Rewrite using trig identities

cos (x) + 3 sin (x) = 3 cos (x)

Subtract

3 cos (x)

from both sides

- 2 cos (x) + 3 sin (x) = 0

Rewrite using trig identities

- 2 + 3 tan (x) = 0

Move

2

to the right side

3 tan (x) = 2

Divide both sides by

3

tan (x) = \frac{2 3}{3}

Apply trig inverse properties

x = arctan (\frac{2 3}{3}) + 18 0^{\circ} n

Show solutions in decimal form

x = 0.85707 \dots + 18 0^{\circ} n

- 33 cot (θ) + 5 = 14

y, d = arctan (\frac{10}{\frac{y}{67} \cdot 1000})

2 arccos (x) = π

- 2 cos (θ) + 1 = 5 cos (θ) + 0

2 sin^{2} (θ) - sin (θ) = 0, 0 \leq θ < 2 π

What is the general solution for 2sin(30+x)=3cos(x) ?
The general solution for 2sin(30+x)=3cos(x) is x=0.85707…+180n