Trigonometry Examples

$y = 4 \cos (π) x$

Step 1

Rewrite the equation as $4 \cos (π) x = y$ .

$4 \cos (π) x = y$

Step 2

Simplify.

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Step 2.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$4 (- \cos (0)) x = y$

Step 2.2

The exact value of $\cos (0)$ is $1$ .

$4 (- 1 \cdot 1) x = y$

Step 2.3

Multiply $- 1$ by $1$ .

$4 \cdot - 1 x = y$

Step 2.4

Multiply $4$ by $- 1$ .

$- 4 x = y$

Step 3

Divide each term in $- 4 x = y$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 x = y$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{y}{- 4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{y}{- 4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{y}{- 4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x = - \frac{y}{4}$