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

The general solution for 2cos(x)+3sin(x)=2 is x=2pin,x=pi-1.17600…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2 πn, x = π - 1.17600 \dots + 2 πn

Solution steps

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

Subtract

3 sin (x)

from both sides

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

Square both sides

(2 cos (x))^{2} = (2 - 3 sin (x))^{2}

Subtract

(2 - 3 sin (x))^{2}

from both sides

4 cos^{2} (x) - 4 + 12 sin (x) - 9 sin^{2} (x) = 0

Rewrite using trig identities

12 sin (x) - 13 sin^{2} (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = \frac{12}{13}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = \frac{12}{13} : x = arcsin (\frac{12}{13}) + 2 πn, x = π - arcsin (\frac{12}{13}) + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arcsin (\frac{12}{13}) + 2 πn, x = π - arcsin (\frac{12}{13}) + 2 πn

Verify solutions by plugging them into the original equation

x = 2 πn, x = π - arcsin (\frac{12}{13}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = π - 1.17600 \dots + 2 πn

- cot (x) - 1 = csc (x)

4 sec (θ) + 1 = 9

4 tan^{2} (x) - 12 = 0

tan (θ) - \frac{1}{3} = 0

tan (\frac{x}{2} + \frac{π}{3}) = 1

What is the general solution for 2cos(x)+3sin(x)=2 ?
The general solution for 2cos(x)+3sin(x)=2 is x=2pin,x=pi-1.17600…+2pin