Trigonometry Examples

$\cos (u) = - \frac{4}{7}$ , $\frac{π}{2} < u < π$

Step 1

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

$u = \arccos (- \frac{4}{7})$

Step 2

Simplify the right side.

Tap for more steps...

Step 2.1

Evaluate $\arccos (- \frac{4}{7})$ .

$u = 2.1790419$

Step 3

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

$u = 2 (3.14159265) - 2.1790419$

Step 4

Solve for $u$ .

Tap for more steps...

Step 4.1

Remove parentheses.

$u = 2 (3.14159265) - 2.1790419$

Step 4.2

Simplify $2 (3.14159265) - 2.1790419$ .

Tap for more steps...

Step 4.2.1

Multiply $2$ by $3.14159265$ .

$u = 6.2831853 - 2.1790419$

Step 4.2.2

Subtract $2.1790419$ from $6.2831853$ .

$u = 4.1041434$

Step 5

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

Tap for more steps...

Step 5.1

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

$\frac{2 π}{| b |}$

Step 5.2

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

$\frac{2 π}{| 1 |}$

Step 5.3

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

$\frac{2 π}{1}$

Step 5.4

Divide $2 π$ by $1$ .

$2 π$

Step 6

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

$u = 2.1790419 + 2 π n, 4.1041434 + 2 π n$ , for any integer $n$

Step 7

Plug in $0$ for $n$ and simplify to see if the solution is contained in $(\frac{π}{2}, π)$ .

Tap for more steps...

Step 7.1

Plug in $0$ for $n$ .

$2.1790419 + 2 π (0)$

Step 7.2

Simplify.

Tap for more steps...

Step 7.2.1

Multiply $2 π (0)$ .

Tap for more steps...

Step 7.2.1.1

Multiply $0$ by $2$ .

$2.1790419 + 0 π$

Step 7.2.1.2

Multiply $0$ by $π$ .

$2.1790419 + 0$

Step 7.2.2

Add $2.1790419$ and $0$ .

$2.1790419$

Step 7.3

The interval $(\frac{π}{2}, π)$ contains $2.1790419$ .

$u = 2.1790419$