Trigonometry Examples

$4 \csc (x - 3) = 1$

Step 1

Divide each term in $4 \csc (x - 3) = 1$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 \csc (x - 3) = 1$ by $4$ .

$\frac{4 \csc (x - 3)}{4} = \frac{1}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 \csc (x - 3)}{4} = \frac{1}{4}$

Step 1.2.1.2

Divide $\csc (x - 3)$ by $1$ .

$\csc (x - 3) = \frac{1}{4}$

Step 2

The range of cosecant is $y \leq - 1$ and $y \geq 1$ . Since $\frac{1}{4}$ does not fall in this range, there is no solution.

No solution