What is the general solution for sin^2(x)-15sin(x)cos(x)+50cos^2(x)=0 ?

The general solution for sin^2(x)-15sin(x)cos(x)+50cos^2(x)=0 is x=1.37340…+pin,x=1.47112…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(x)-15sin(x)cos(x)+50cos^2(x)=0

sin^{2} (x) - 15 sin (x) cos (x) + 50 cos^{2} (x) = 0

x = 1.37340 \dots + πn, x = 1.47112 \dots + πn

Solution steps

sin^{2} (x) - 15 sin (x) cos (x) + 50 cos^{2} (x) = 0

Factor

sin^{2} (x) - 15 sin (x) cos (x) + 50 cos^{2} (x) : (sin (x) - 5 cos (x)) (sin (x) - 10 cos (x))

(sin (x) - 5 cos (x)) (sin (x) - 10 cos (x)) = 0

Solving each part separately

sin (x) - 5 cos (x) = 0 or sin (x) - 10 cos (x) = 0

sin (x) - 5 cos (x) = 0 : x = arctan (5) + πn

sin (x) - 10 cos (x) = 0 : x = arctan (10) + πn

Combine all the solutions

x = arctan (5) + πn, x = arctan (10) + πn

Show solutions in decimal form

x = 1.37340 \dots + πn, x = 1.47112 \dots + πn

cot (x) = sin^{2} (x)

sec (2 x + 60) = - 1.5

sin^{2} (x) + 2 sin^{2} (\frac{x}{2}) = 1

tan (a) = 0.7

8 sin (x) - 4 csc (x) = 0

What is the general solution for sin^2(x)-15sin(x)cos(x)+50cos^2(x)=0 ?
The general solution for sin^2(x)-15sin(x)cos(x)+50cos^2(x)=0 is x=1.37340…+pin,x=1.47112…+pin