Trigonometry Examples

cos (B) = \frac{{(7)}^{2} + {(10.35513349)}^{2} - {(12)}^{2}}{2 (7) (10.35513349)}

$\cos (B) = \frac{{(7)}^{2} + {(10.35513349)}^{2} - {(12)}^{2}}{2 (7) (10.35513349)}$

Step 1

Simplify

\frac{7^{2} + {10.35513349}^{2} - 12^{2}}{2 (7) \cdot 10.35513349}

$\frac{7^{2} + {10.35513349}^{2} - 12^{2}}{2 (7) \cdot 10.35513349}$ .

Tap for more steps...

Step 1.1

Simplify the numerator.

Tap for more steps...

Step 1.1.1

Raise

7

$7$ to the power of

2

$2$ .

cos (B) = \frac{49 + {10.35513349}^{2} - 12^{2}}{2 (7) \cdot 10.35513349}

$\cos (B) = \frac{49 + {10.35513349}^{2} - 12^{2}}{2 (7) \cdot 10.35513349}$

Step 1.1.2

Raise

10.35513349

$10.35513349$ to the power of

2

$2$ .

cos (B) = \frac{49 + 107.22878959 - 12^{2}}{2 (7) \cdot 10.35513349}

$\cos (B) = \frac{49 + 107.22878959 - 12^{2}}{2 (7) \cdot 10.35513349}$

Step 1.1.3

Raise

12

$12$ to the power of

2

$2$ .

cos (B) = \frac{49 + 107.22878959 - 1 \cdot 144}{2 (7) \cdot 10.35513349}

$\cos (B) = \frac{49 + 107.22878959 - 1 \cdot 144}{2 (7) \cdot 10.35513349}$

Step 1.1.4

Multiply

- 1

$- 1$ by

144

$144$ .

cos (B) = \frac{49 + 107.22878959 - 144}{2 (7) \cdot 10.35513349}

$\cos (B) = \frac{49 + 107.22878959 - 144}{2 (7) \cdot 10.35513349}$

Step 1.1.5

Add

49

$49$ and

107.22878959

$107.22878959$ .

cos (B) = \frac{156.22878959 - 144}{2 (7) \cdot 10.35513349}

$\cos (B) = \frac{156.22878959 - 144}{2 (7) \cdot 10.35513349}$

Step 1.1.6

Subtract

144

$144$ from

156.22878959

$156.22878959$ .

cos (B) = \frac{12.22878959}{2 (7) \cdot 10.35513349}

$\cos (B) = \frac{12.22878959}{2 (7) \cdot 10.35513349}$

cos (B) = \frac{12.22878959}{2 (7) \cdot 10.35513349}

$\cos (B) = \frac{12.22878959}{2 (7) \cdot 10.35513349}$

Step 1.2

Simplify the denominator.

Tap for more steps...

Step 1.2.1

Multiply

2

$2$ by

7

$7$ .

cos (B) = \frac{12.22878959}{14 \cdot 10.35513349}

$\cos (B) = \frac{12.22878959}{14 \cdot 10.35513349}$

Step 1.2.2

Multiply

14

$14$ by

10.35513349

$10.35513349$ .

cos (B) = \frac{12.22878959}{144.97186886}

$\cos (B) = \frac{12.22878959}{144.97186886}$

cos (B) = \frac{12.22878959}{144.97186886}

$\cos (B) = \frac{12.22878959}{144.97186886}$

Step 1.3

Divide

12.22878959

$12.22878959$ by

144.97186886

$144.97186886$ .

cos (B) = 0.08435284

$\cos (B) = 0.08435284$

cos (B) = 0.08435284

$\cos (B) = 0.08435284$

Step 2

Take the inverse cosine of both sides of the equation to extract

B

$B$ from inside the cosine.

B = arccos (0.08435284)

$B = \arccos (0.08435284)$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Evaluate

arccos (0.08435284)

$\arccos (0.08435284)$ .

B = 1.48634312

$B = 1.48634312$

B = 1.48634312

$B = 1.48634312$

Step 4

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

2 π

$2 π$ to find the solution in the fourth quadrant.

B = 2 (3.14159265) - 1.48634312

$B = 2 (3.14159265) - 1.48634312$

Step 5

Simplify

2 (3.14159265) - 1.48634312

$2 (3.14159265) - 1.48634312$ .

Tap for more steps...

Step 5.1

Multiply

2

$2$ by

3.14159265

$3.14159265$ .

B = 6.2831853 - 1.48634312

$B = 6.2831853 - 1.48634312$

Step 5.2

Subtract

1.48634312

$1.48634312$ from

6.2831853

$6.2831853$ .

B = 4.79684218

$B = 4.79684218$

B = 4.79684218

$B = 4.79684218$

Step 6

Find the period of

cos (B)

$\cos (B)$ .

Tap for more steps...

Step 6.1

The period of the function can be calculated using

\frac{2 π}{| b |}

$\frac{2 π}{| b |}$ .

\frac{2 π}{| b |}

$\frac{2 π}{| b |}$

Step 6.2

Replace

b

$b$ with

1

$1$ in the formula for period.

\frac{2 π}{| 1 |}

$\frac{2 π}{| 1 |}$

Step 6.3

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

0

$0$ and

1

$1$ is

1

$1$ .

\frac{2 π}{1}

$\frac{2 π}{1}$

Step 6.4

Divide

2 π

$2 π$ by

1

$1$ .

2 π

$2 π$

2 π

$2 π$

Step 7

The period of the

cos (B)

$\cos (B)$ function is

2 π

$2 π$ so values will repeat every

2 π

$2 π$ radians in both directions.

B = 1.48634312 + 2 π n, 4.79684218 + 2 π n

$B = 1.48634312 + 2 π n, 4.79684218 + 2 π n$ , for any integer

n

$n$