Trigonometry Examples

$f (x) = 0.6 \sin (\frac{2 π}{5} x)$ , $f (x) = 150$

Step 1

Substitute $150$ for $f (x)$ .

$150 = 0.6 \sin (\frac{2 π}{5} x)$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $0.6 \sin (\frac{2 π}{5} x) = 150$ .

$0.6 \sin (\frac{2 π}{5} x) = 150$

Step 2.2

Divide each term in $0.6 \sin (\frac{2 π}{5} x) = 150$ by $0.6$ and simplify.

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Step 2.2.1

Divide each term in $0.6 \sin (\frac{2 π}{5} x) = 150$ by $0.6$ .

$\frac{0.6 \sin (\frac{2 π}{5} x)}{0.6} = \frac{150}{0.6}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $0.6$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{0.6 \sin (\frac{2 π}{5} x)}{0.6} = \frac{150}{0.6}$

Step 2.2.2.1.2

Divide $\sin (\frac{2 π}{5} x)$ by $1$ .

$\sin (\frac{2 π}{5} x) = \frac{150}{0.6}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $150$ by $0.6$ .

$\sin (\frac{2 π}{5} x) = 250$

Step 2.3

The range of sine is $- 1 \leq y \leq 1$ . Since $250$ does not fall in this range, there is no solution.

No solution