What is the general solution for sin(2x)+cos(x)=0,x<= 2pi,0 ?

The general solution for sin(2x)+cos(x)=0,x<= 2pi,0 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x)+cos(x)=0,x<= 2pi,0

sin (2 x) + cos (x) = 0, x \leq 2 π, 0

x = \frac{π}{2}, x = \frac{3 π}{2}, x = - \frac{3 π}{2}, x = - \frac{π}{2}, x = - \frac{7 π}{2}, x = - \frac{5 π}{2}, x = - \frac{11 π}{2}, x = - \frac{9 π}{2}, x = - \frac{15 π}{2}, x = - \frac{13 π}{2}, x = \frac{7 π}{6}, x = \frac{11 π}{6}, x = - \frac{5 π}{6}, x = - \frac{π}{6}, x = - \frac{17 π}{6}, x = - \frac{13 π}{6}, x = - \frac{29 π}{6}, x = - \frac{25 π}{6}, x = - \frac{41 π}{6}, x = - \frac{37 π}{6}

Solution steps

sin (2 x) + cos (x) = 0, x \leq 2 π, 0

Rewrite using trig identities

cos (x) + 2 cos (x) sin (x) = 0

Factor

cos (x) + 2 cos (x) sin (x) : cos (x) (2 sin (x) + 1)

cos (x) (2 sin (x) + 1) = 0

Solving each part separately

cos (x) = 0 or 2 sin (x) + 1 = 0

cos (x) = 0, x \leq 2 π : x = \frac{π}{2}, x = \frac{3 π}{2}, x = - \frac{3 π}{2}, x = - \frac{π}{2}, x = - \frac{7 π}{2}, x = - \frac{5 π}{2}, x = - \frac{11 π}{2}, x = - \frac{9 π}{2}, x = - \frac{15 π}{2}, x = - \frac{13 π}{2}

2 sin (x) + 1 = 0, x \leq 2 π : x = \frac{7 π}{6}, x = \frac{11 π}{6}, x = - \frac{5 π}{6}, x = - \frac{π}{6}, x = - \frac{17 π}{6}, x = - \frac{13 π}{6}, x = - \frac{29 π}{6}, x = - \frac{25 π}{6}, x = - \frac{41 π}{6}, x = - \frac{37 π}{6}

Combine all the solutions

x = \frac{π}{2}, x = \frac{3 π}{2}, x = - \frac{3 π}{2}, x = - \frac{π}{2}, x = - \frac{7 π}{2}, x = - \frac{5 π}{2}, x = - \frac{11 π}{2}, x = - \frac{9 π}{2}, x = - \frac{15 π}{2}, x = - \frac{13 π}{2}, x = \frac{7 π}{6}, x = \frac{11 π}{6}, x = - \frac{5 π}{6}, x = - \frac{π}{6}, x = - \frac{17 π}{6}, x = - \frac{13 π}{6}, x = - \frac{29 π}{6}, x = - \frac{25 π}{6}, x = - \frac{41 π}{6}, x = - \frac{37 π}{6}

6 sin (x) = 5 cos (x)

sin (θ) = \frac{- 3}{4}

2 csc (θ) + 3 sec (θ) = 0

6 + 9 cos (x) = 2 sin^{2} (x)

tan (2 θ) = \frac{77}{51 - 20}

What is the general solution for sin(2x)+cos(x)=0,x<= 2pi,0 ?
The general solution for sin(2x)+cos(x)=0,x<= 2pi,0 is