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

The general solution for sin^2(x)+4cos^2(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(x)+4cos^2(x)=1

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

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

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

= 4 cos^{2} (x) - cos^{2} (x)

Simplify

= 3 cos^{2} (x)

3 cos^{2} (x) = 0

Divide both sides by

3

3 cos^{2} (x) = 0

Divide both sides by

3

3 cos^{2} (x) = 0

Divide both sides by

3

\frac{3 cos ^{2} ( x )}{3} = \frac{0}{3}

Simplify

cos^{2} (x) = 0

cos^{2} (x) = 0

Apply rule

x^{n} = 0 \Rightarrow x = 0

cos (x) = 0

General solutions for

cos (x) = 0

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

4 cos (x^{2}) - 3 = 0

sin (x) + 1 = 0, 0 \leq x < 2 π

θ, sin^{2} (θ) = \frac{1}{4}

cot (θ) = 3, 0 \leq θ < 2 π

(2 cos (2 θ)) = 2

What is the general solution for sin^2(x)+4cos^2(x)=1 ?
The general solution for sin^2(x)+4cos^2(x)=1 is x= pi/2+2pin,x=(3pi)/2+2pin