Trigonometry Examples

$3 \csc (A) - 2 \sin (A) - 5 = 0$

Step 1

Simplify $3 \csc (A) - 2 \sin (A) - 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite $\csc (A)$ in terms of sines and cosines.

$3 \frac{1}{\sin (A)} - 2 \sin (A) - 5 = 0$

Step 1.1.2

Combine $3$ and $\frac{1}{\sin (A)}$ .

$\frac{3}{\sin (A)} - 2 \sin (A) - 5 = 0$

Step 1.2

Simplify each term.

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Step 1.2.1

Separate fractions.

$\frac{3}{1} \cdot \frac{1}{\sin (A)} - 2 \sin (A) - 5 = 0$

Step 1.2.2

Convert from $\frac{1}{\sin (A)}$ to $\csc (A)$ .

$\frac{3}{1} \csc (A) - 2 \sin (A) - 5 = 0$

Step 1.2.3

Divide $3$ by $1$ .

$3 \csc (A) - 2 \sin (A) - 5 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$A = \frac{π}{6} + 2 π n, \frac{5 π}{6} + 2 π n$ , for any integer $n$

Step 3