What is the general solution for sin(2x)-cos^2(x)=0 ?

The general solution for sin(2x)-cos^2(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x=0.46364…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.46364 \dots + πn

Solution steps

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

Rewrite using trig identities

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

Factor

- cos^{2} (x) + 2 cos (x) sin (x) : cos (x) (- cos (x) + 2 sin (x))

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

Solving each part separately

cos (x) = 0 or - cos (x) + 2 sin (x) = 0

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

- cos (x) + 2 sin (x) = 0 : x = arctan (\frac{1}{2}) + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.46364 \dots + πn

2 sin (\frac{π x}{2}) + 1 = 0

sin (x) = 0.819

tan (x) = 1.1

sin (x) = 45

sin (x) = 90

What is the general solution for sin(2x)-cos^2(x)=0 ?
The general solution for sin(2x)-cos^2(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin,x=0.46364…+pin