What is the general solution for sqrt(2)*sin^2(x)+cos(x)=0 ?

The general solution for sqrt(2)*sin^2(x)+cos(x)=0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(2)*sin^2(x)+cos(x)=0

2 \cdot sin^{2} (x) + cos (x) = 0

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Solution steps

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

Rewrite using trig identities

cos (x) + (1 - cos^{2} (x)) 2 = 0

Solve by substitution

cos (x) = - \frac{2}{2}, cos (x) = 2

cos (x) = - \frac{2}{2} : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

cos (x) = 2 :

No Solution

Combine all the solutions

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

cot (x) = - 7.77

tan (θ) = \frac{5}{10}

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

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

2 sin^{2} (θ) - 5 sin (θ) - 3 = 0

What is the general solution for sqrt(2)*sin^2(x)+cos(x)=0 ?
The general solution for sqrt(2)*sin^2(x)+cos(x)=0 is x=(3pi)/4+2pin,x=(5pi)/4+2pin