Basic Math Examples

$- 3.51 = \tan (3.74 t)$

Step 1

Rewrite the equation as $\tan (3.74 t) = - 3.51$ .

$\tan (3.74 t) = - 3.51$

Step 2

Take the inverse tangent of both sides of the equation to extract $t$ from inside the tangent.

$3.74 t = \arctan (- 3.51)$

Step 3

Simplify the right side.

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Step 3.1

Evaluate $\arctan (- 3.51)$ .

$3.74 t = - 1.29324939$

Step 4

Divide each term in $3.74 t = - 1.29324939$ by $3.74$ and simplify.

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Step 4.1

Divide each term in $3.74 t = - 1.29324939$ by $3.74$ .

$\frac{3.74 t}{3.74} = \frac{- 1.29324939}{3.74}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3.74$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3.74 t}{3.74} = \frac{- 1.29324939}{3.74}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 1.29324939}{3.74}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 1.29324939$ by $3.74$ .

$t = - 0.3457886$

Step 5

The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from $π$ to find the solution in the third quadrant.

$3.74 t = - 1.29324939 - (3.14159265)$

Step 6

Simplify the expression to find the second solution.

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Step 6.1

Add $2 π$ to $- 1.29324939 - (3.14159265)$ .

$3.74 t = - 1.29324939 - (3.14159265) + 2 π$

Step 6.2

The resulting angle of $1.84834325$ is positive and coterminal with $- 1.29324939 - (3.14159265)$ .

$3.74 t = 1.84834325$

Step 6.3

Divide each term in $3.74 t = 1.84834325$ by $3.74$ and simplify.

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Step 6.3.1

Divide each term in $3.74 t = 1.84834325$ by $3.74$ .

$\frac{3.74 t}{3.74} = \frac{1.84834325}{3.74}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $3.74$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{3.74 t}{3.74} = \frac{1.84834325}{3.74}$

Step 6.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{1.84834325}{3.74}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Divide $1.84834325$ by $3.74$ .

$t = 0.49420942$

Step 7

Find the period of $\tan (3.74 t)$ .

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Step 7.1

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

$\frac{π}{| b |}$

Step 7.2

Replace $b$ with $3.74$ in the formula for period.

$\frac{π}{| 3.74 |}$

Step 7.3

The absolute value is the distance between a number and zero. The distance between $0$ and $3.74$ is $3.74$ .

$\frac{π}{3.74}$

Step 7.4

Replace $π$ with an approximation.

$\frac{3.14159265}{3.74}$

Step 7.5

Divide $3.14159265$ by $3.74$ .

$0.83999803$

Step 8

Add $0.83999803$ to every negative angle to get positive angles.

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Step 8.1

Add $0.83999803$ to $- 0.3457886$ to find the positive angle.

$- 0.3457886 + 0.83999803$

Step 8.2

Subtract $0.3457886$ from $0.83999803$ .

$0.49420942$

Step 8.3

List the new angles.

$t = 0.49420942$

Step 9

The period of the $\tan (3.74 t)$ function is $0.83999803$ so values will repeat every $0.83999803$ radians in both directions.

$t = 0.49420942 + 0.83999803 n, 0.49420942 + 0.83999803 n$ , for any integer $n$

Step 10

Consolidate $0.49420942 + 0.83999803 n$ and $0.49420942 + 0.83999803 n$ to $0.49420942 + 0.83999803 n$ .

$t = 0.49420942 + 0.83999803 n$ , for any integer $n$