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Solve for all values of thetaθ, such that 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , rounding all values to the nearest tenth.6, cosecant, theta, plus, 6, equals, 06cscθ+6=0

Question

Solve for all values of thetaθ, such that 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , rounding all values to the nearest tenth.6, cosecant, theta, plus, 6, equals, 06cscθ+6=0

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Solution

To solve the equation 6cscθ + 6 = 0 for 0 ≤ θ < 360, follow these steps:

  1. First, isolate cscθ by subtracting 6 from both sides of the equation:

    6cscθ = -6

  2. Then, divide both sides by 6 to solve for cscθ:

    cscθ = -1

  3. The cosecant function is the reciprocal of the sine function. So, this equation is equivalent to sinθ = -1.

  4. The sine function equals -1 at θ = 270 degrees in the interval 0 ≤ θ < 360.

So, the solution to the equation 6cscθ + 6 = 0 for 0 ≤ θ < 360 is θ = 270 degrees.

This problem has been solved

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