Trigonometry Examples

$4 \cdot (\cos (\frac{1}{2}) (x - π)) - 1 = 2$

Step 1

Simplify the left side.

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Step 1.1

Simplify $4 \cdot (\cos (\frac{1}{2}) (x - π)) - 1$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Evaluate $\cos (\frac{1}{2})$ .

$4 \cdot (0.87758256 (x - π)) - 1 = 2$

Step 1.1.1.2

Apply the distributive property.

$4 \cdot (0.87758256 x + 0.87758256 (- π)) - 1 = 2$

Step 1.1.1.3

Multiply $0.87758256 (- π)$ .

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Step 1.1.1.3.1

Multiply $- 1$ by $0.87758256$ .

$4 \cdot (0.87758256 x - 0.87758256 π) - 1 = 2$

Step 1.1.1.3.2

Multiply $- 0.87758256$ by $π$ .

$4 \cdot (0.87758256 x - 2.75700692) - 1 = 2$

Step 1.1.1.4

Apply the distributive property.

$4 (0.87758256 x) + 4 \cdot - 2.75700692 - 1 = 2$

Step 1.1.1.5

Multiply $0.87758256$ by $4$ .

$3.51033024 x + 4 \cdot - 2.75700692 - 1 = 2$

Step 1.1.1.6

Multiply $4$ by $- 2.75700692$ .

$3.51033024 x - 11.02802771 - 1 = 2$

Step 1.1.2

Subtract $1$ from $- 11.02802771$ .

$3.51033024 x - 12.02802771 = 2$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $12.02802771$ to both sides of the equation.

$3.51033024 x = 2 + 12.02802771$

Step 2.2

Add $2$ and $12.02802771$ .

$3.51033024 x = 14.02802771$

Step 3

Divide each term in $3.51033024 x = 14.02802771$ by $3.51033024$ and simplify.

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Step 3.1

Divide each term in $3.51033024 x = 14.02802771$ by $3.51033024$ .

$\frac{3.51033024 x}{3.51033024} = \frac{14.02802771}{3.51033024}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3.51033024$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3.51033024 x}{3.51033024} = \frac{14.02802771}{3.51033024}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{14.02802771}{3.51033024}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $14.02802771$ by $3.51033024$ .

$x = 3.99621309$