What is the general solution for 4sin(x)-cos(2x)=1 ?

The general solution for 4sin(x)-cos(2x)=1 is x=0.42707…+2pin,x=pi-0.42707…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4sin(x)-cos(2x)=1

4 sin (x) - cos (2 x) = 1

x = 0.42707 \dots + 2 πn, x = π - 0.42707 \dots + 2 πn

Solution steps

4 sin (x) - cos (2 x) = 1

Subtract

1

from both sides

4 sin (x) - cos (2 x) - 1 = 0

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 1 + 2, sin (x) = - 1 - 2

sin (x) = - 1 + 2 : x = arcsin (- 1 + 2) + 2 πn, x = π - arcsin (- 1 + 2) + 2 πn

sin (x) = - 1 - 2 :

No Solution

Combine all the solutions

x = arcsin (- 1 + 2) + 2 πn, x = π - arcsin (- 1 + 2) + 2 πn

Show solutions in decimal form

x = 0.42707 \dots + 2 πn, x = π - 0.42707 \dots + 2 πn

2 sin^{2} (t) - 3 sin (t) + 1 = 0

5 sin (x) = 0

5 sin (x) = 4

5 sin (x) = 3

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

What is the general solution for 4sin(x)-cos(2x)=1 ?
The general solution for 4sin(x)-cos(2x)=1 is x=0.42707…+2pin,x=pi-0.42707…+2pin