What is the general solution for 7cot(θ)=3csc(θ) ?

The general solution for 7cot(θ)=3csc(θ) is θ=1.12788…+2pin,θ=2pi-1.12788…+2pin

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7cot(θ)=3csc(θ)

7 cot (θ) = 3 csc (θ)

θ = 1.12788 \dots + 2 πn, θ = 2 π - 1.12788 \dots + 2 πn

Solution steps

7 cot (θ) = 3 csc (θ)

Subtract

3 csc (θ)

from both sides

7 cot (θ) - 3 csc (θ) = 0

Express with sin, cos

\frac{- 3 + 7 cos ( θ )}{sin ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- 3 + 7 cos (θ) = 0

Move

3

to the right side

7 cos (θ) = 3

Divide both sides by

7

cos (θ) = \frac{3}{7}

Apply trig inverse properties

θ = arccos (\frac{3}{7}) + 2 πn, θ = 2 π - arccos (\frac{3}{7}) + 2 πn

Show solutions in decimal form

θ = 1.12788 \dots + 2 πn, θ = 2 π - 1.12788 \dots + 2 πn

5 sin (x) = 2

4 (cot (θ) + 1) = 2 (cot (θ) + 2)

sin (3 t) = 0

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

csc^{2} (x) = 0

What is the general solution for 7cot(θ)=3csc(θ) ?
The general solution for 7cot(θ)=3csc(θ) is θ=1.12788…+2pin,θ=2pi-1.12788…+2pin