What is the general solution for cos(2x)-3sin(x)=2,0<= x<= 360 ?

The general solution for cos(2x)-3sin(x)=2,0<= x<= 360 is x=270,x=210,x=330

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(2x)-3sin(x)=2,0<= x<= 360

cos (2 x) - 3 sin (x) = 2, 0^{\circ} \leq x \leq 36 0^{\circ}

x = 27 0^{\circ}, x = 21 0^{\circ}, x = 33 0^{\circ}

Solution steps

cos (2 x) - 3 sin (x) = 2, 0^{\circ} \leq x \leq 36 0^{\circ}

Subtract

2

from both sides

cos (2 x) - 3 sin (x) - 2 = 0

Rewrite using trig identities

- 1 - 2 sin^{2} (x) - 3 sin (x) = 0

Solve by substitution

sin (x) = - 1, sin (x) = - \frac{1}{2}

sin (x) = - 1, 0 \leq x \leq 36 0^{\circ} : x = 27 0^{\circ}

sin (x) = - \frac{1}{2}, 0 \leq x \leq 36 0^{\circ} : x = 21 0^{\circ}, x = 33 0^{\circ}

Combine all the solutions

x = 27 0^{\circ}, x = 21 0^{\circ}, x = 33 0^{\circ}

2 cos^{2} (x) + 3 cos (x) = 4 cos (x) + 1

6 sin^{2} (x) + 5 sin (x) = 0

sin (x) = - \frac{1}{2}, (0, 2 π)

tan (θ) = \frac{4}{3}, cos (θ) < 0

cot (x) = \frac{sin ( x )}{cos ( x )}

What is the general solution for cos(2x)-3sin(x)=2,0<= x<= 360 ?
The general solution for cos(2x)-3sin(x)=2,0<= x<= 360 is x=270,x=210,x=330