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

The general solution for 2cos(x)+1=sin(x) is x= pi/2+2pin,x=-2.49809…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(x)+1=sin(x)

2 cos (x) + 1 = sin (x)

x = \frac{π}{2} + 2 πn, x = - 2.49809 \dots + 2 πn

Solution steps

2 cos (x) + 1 = sin (x)

Square both sides

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

4 cos (x) + 5 cos^{2} (x) = 0

Solve by substitution

cos (x) = 0, cos (x) = - \frac{4}{5}

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = - \frac{4}{5} : x = arccos (- \frac{4}{5}) + 2 πn, x = - arccos (- \frac{4}{5}) + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arccos (- \frac{4}{5}) + 2 πn, x = - arccos (- \frac{4}{5}) + 2 πn

Verify solutions by plugging them into the original equation

x = \frac{π}{2} + 2 πn, x = - arccos (- \frac{4}{5}) + 2 πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = - 2.49809 \dots + 2 πn

csc^{2} (x) = 2 csc (x)

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

2 cos (4 x) + 3 = 4 cos (2 x)

sinh (y) = 0

2 + 2 cos (θ) = 4

What is the general solution for 2cos(x)+1=sin(x) ?
The general solution for 2cos(x)+1=sin(x) is x= pi/2+2pin,x=-2.49809…+2pin