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

The general solution for 4cos(x)=3sin(x) is x=0.92729…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos(x)=3sin(x)

4 cos (x) = 3 sin (x)

x = 0.92729 \dots + πn

Degrees

x = 53.13010 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 cos (x) = 3 sin (x)

Rewrite using trig identities

4 cos (x) = 3 sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

4 = 3 tan (x)

Switch sides

3 tan (x) = 4

3 tan (x) = 4

Divide both sides by

3

3 tan (x) = 4

Divide both sides by

3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (\frac{4}{3}) + πn

x = arctan (\frac{4}{3}) + πn

Show solutions in decimal form

x = 0.92729 \dots + πn

cos (π x) = 0, 0 \leq x \leq 2 π

cos (2 x - 1 5^{\circ}) = - sin (6 0^{\circ} - 3 x)

4 sin^{2} (x) - cos (x) - 1 = 0

tan (\frac{θ}{2} - \frac{π}{4}) = 1, 0 \leq θ < 2 π

1 + cos^{2} (x^{2} + 1) = sin^{2} (x^{2} + 1)

What is the general solution for 4cos(x)=3sin(x) ?
The general solution for 4cos(x)=3sin(x) is x=0.92729…+pin