What is the general solution for 4sin(x)-3cos(x)=0 ?

The general solution for 4sin(x)-3cos(x)=0 is x=0.64350…+pin

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4sin(x)-3cos(x)=0

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

x = 0.64350 \dots + πn

Degrees

x = 36.86989 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{4 sin ( x ) - 3 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{4 sin ( x )}{cos ( x )} - 3 = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

4 tan (x) - 3 = 0

4 tan (x) - 3 = 0

Move

3

to the right side

4 tan (x) - 3 = 0

Add

3

to both sides

4 tan (x) - 3 + 3 = 0 + 3

Simplify

4 tan (x) = 3

4 tan (x) = 3

Divide both sides by

4

4 tan (x) = 3

Divide both sides by

4

\frac{4 tan ( x )}{4} = \frac{3}{4}

Simplify

tan (x) = \frac{3}{4}

tan (x) = \frac{3}{4}

Apply trig inverse properties

tan (x) = \frac{3}{4}

General solutions for

tan (x) = \frac{3}{4}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{3}{4}) + πn

x = arctan (\frac{3}{4}) + πn

Show solutions in decimal form

x = 0.64350 \dots + πn

25 cos^{2} (3 x) + 10 cos (3 x) = 15

5 cos^{2} (x) = 6 sin (x)

sec^{2} (x) = 2 tan (x) + 4

- 4 cos (θ) = - sin^{2} (θ) + 1

2 sin^{2} (θ) + 3 sin (θ) = 0, 0 \leq θ < 2 π

What is the general solution for 4sin(x)-3cos(x)=0 ?
The general solution for 4sin(x)-3cos(x)=0 is x=0.64350…+pin