What is the general solution for sin(θ)=csc(θ) ?

The general solution for sin(θ)=csc(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(θ)=csc(θ)

sin (θ) = csc (θ)

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

Solution steps

sin (θ) = csc (θ)

Subtract

csc (θ)

from both sides

sin (θ) - csc (θ) = 0

Rewrite using trig identities

- csc (θ) + \frac{1}{csc ( θ )} = 0

Solve by substitution

csc (θ) = 1, csc (θ) = - 1

csc (θ) = 1 : θ = \frac{π}{2} + 2 πn

csc (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

- 5 sin (x) = 0, 0 \leq x \leq 2 π

3 sec^{2} (θ) - 4 = 0

(cot (x) + 1) (3 tan (x) + 1) = 0

0 = 2 cos (x) - 1

4 sin (2 x) = 2

What is the general solution for sin(θ)=csc(θ) ?
The general solution for sin(θ)=csc(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin