Trigonometry Examples

$\sin (40) = \frac{4}{a}$

Step 1

Rewrite the equation as $\frac{4}{a} = \sin (40)$ .

$\frac{4}{a} = \sin (40)$

Step 2

Evaluate $\sin (40)$ .

$\frac{4}{a} = 0.6427876$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a, 1$

Step 3.2

The LCM of one and any expression is the expression.

$a$

Step 4

Multiply each term in $\frac{4}{a} = 0.6427876$ by $a$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{4}{a} = 0.6427876$ by $a$ .

$\frac{4}{a} a = 0.6427876 a$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $a$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4}{a} a = 0.6427876 a$

Step 4.2.1.2

Rewrite the expression.

$4 = 0.6427876 a$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $0.6427876 a = 4$ .

$0.6427876 a = 4$

Step 5.2

Divide each term in $0.6427876 a = 4$ by $0.6427876$ and simplify.

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Step 5.2.1

Divide each term in $0.6427876 a = 4$ by $0.6427876$ .

$\frac{0.6427876 a}{0.6427876} = \frac{4}{0.6427876}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $0.6427876$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{0.6427876 a}{0.6427876} = \frac{4}{0.6427876}$

Step 5.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{4}{0.6427876}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $4$ by $0.6427876$ .

$a = 6.2228953$