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

The general solution for sin^2(x)+cos^2(x)+cos(x)=2 is x=2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

= cos (x) + 1

cos (x) + 1 = 2

Move

1

to the right side

cos (x) + 1 = 2

Subtract

1

from both sides

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

Simplify

cos (x) = 1

cos (x) = 1

General solutions for

cos (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

\frac{sin ^{3} ( x )}{sin ( x )} = 0

sin (135 - x) = sin (x)

tan (x) - 4 = - 1

4 cos^{2} (x) - 8 cos (x) + 3 = 0

sin (2 x) = - 0.6

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