What is the general solution for 6csc(θ)+7=0 ?

The general solution for 6csc(θ)+7=0 is θ=-1.02969…+2pin,θ=pi+1.02969…+2pin

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6csc(θ)+7=0

6 csc (θ) + 7 = 0

θ = - 1.02969 \dots + 2 πn, θ = π + 1.02969 \dots + 2 πn

Degrees

θ = - 58.99728 \dots^{\circ} + 36 0^{\circ} n, θ = 238.99728 \dots^{\circ} + 36 0^{\circ} n

Solution steps

6 csc (θ) + 7 = 0

Move

7

to the right side

6 csc (θ) + 7 = 0

Subtract

7

from both sides

6 csc (θ) + 7 - 7 = 0 - 7

Simplify

6 csc (θ) = - 7

6 csc (θ) = - 7

Divide both sides by

6

6 csc (θ) = - 7

Divide both sides by

6

\frac{6 csc ( θ )}{6} = \frac{- 7}{6}

Simplify

csc (θ) = - \frac{7}{6}

csc (θ) = - \frac{7}{6}

Apply trig inverse properties

csc (θ) = - \frac{7}{6}

General solutions for

csc (θ) = - \frac{7}{6}

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

θ = arccsc (- \frac{7}{6}) + 2 πn, θ = π + arccsc (\frac{7}{6}) + 2 πn

θ = arccsc (- \frac{7}{6}) + 2 πn, θ = π + arccsc (\frac{7}{6}) + 2 πn

Show solutions in decimal form

θ = - 1.02969 \dots + 2 πn, θ = π + 1.02969 \dots + 2 πn

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

cos (5 x) cos (3 x) - sin (5 x) sin (3 x) = \frac{3}{2}

- 6 sin (2 x) = 0

sin (3 x) - 1 = 0

- sin (θ) = 0

What is the general solution for 6csc(θ)+7=0 ?
The general solution for 6csc(θ)+7=0 is θ=-1.02969…+2pin,θ=pi+1.02969…+2pin