What is the general solution for sin(x)*cos(x)-3cos(x)=0 ?

The general solution for sin(x)*cos(x)-3cos(x)=0 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(x)*cos(x)-3cos(x)=0

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

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

Factor

sin (x) cos (x) - 3 cos (x) : cos (x) (sin (x) - 3)

sin (x) cos (x) - 3 cos (x)

Factor out common term

cos (x)

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

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

Solving each part separately

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

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

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

sin (x) - 3 = 0 :

No Solution

sin (x) - 3 = 0

Move

3

to the right side

sin (x) - 3 = 0

Add

3

to both sides

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

Simplify

sin (x) = 3

sin (x) = 3

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

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

9.8 \cdot sin (α) - 0.2 \cdot 9.8 \cdot cos (α) = 0.47

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

tan^{2} (θ) = \frac{sin ^{2} ( θ )}{cos ( θ )}

tan (x) = 1, 17

θ, 2 cot (θ) - 1 = 0

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