Trigonometry Examples

$- 6 = - 6 \cos (A)$

Step 1

Rewrite the equation as $- 6 \cos (A) = - 6$ .

$- 6 \cos (A) = - 6$

Step 2

Divide each term in $- 6 \cos (A) = - 6$ by $- 6$ and simplify.

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Step 2.1

Divide each term in $- 6 \cos (A) = - 6$ by $- 6$ .

$\frac{- 6 \cos (A)}{- 6} = \frac{- 6}{- 6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 6 \cos (A)}{- 6} = \frac{- 6}{- 6}$

Step 2.2.1.2

Divide $\cos (A)$ by $1$ .

$\cos (A) = \frac{- 6}{- 6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 6$ by $- 6$ .

$\cos (A) = 1$

Step 3

Take the inverse cosine of both sides of the equation to extract $A$ from inside the cosine.

$A = \arccos (1)$

Step 4

Simplify the right side.

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Step 4.1

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

$A = 0$

Step 5

The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from $2 π$ to find the solution in the fourth quadrant.

$A = 2 π - 0$

Step 6

Subtract $0$ from $2 π$ .

$A = 2 π$

Step 7

Find the period of $\cos (A)$ .

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Step 7.1

The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Step 7.2

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

Step 7.3

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Step 7.4

Divide $2 π$ by $1$ .

$2 π$

Step 8

The period of the $\cos (A)$ function is $2 π$ so values will repeat every $2 π$ radians in both directions.

$A = 2 π n, 2 π + 2 π n$ , for any integer $n$

Step 9

Consolidate the answers.

$A = 2 π n$ , for any integer $n$