Trigonometry Examples

$\arcsin (n) (- \frac{5}{2} \cdot π) + \frac{a}{2} \cdot \cos (8 π) - (\frac{a}{2} + 1) \cos (0)$

Step 1

Simplify each term.

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Step 1.1

Combine

$π$ and

$\frac{5}{2}$ .

$\arcsin (n) (- \frac{π \cdot 5}{2}) + \frac{a}{2} \cdot \cos (8 π) - (\frac{a}{2} + 1) \cos (0)$

Step 1.2

Move

$5$ to the left of

$π$ .

$\arcsin (n) (- \frac{5 \cdot π}{2}) + \frac{a}{2} \cdot \cos (8 π) - (\frac{a}{2} + 1) \cos (0)$

Step 1.3

Combine

$\arcsin (n)$ and

$\frac{5 π}{2}$ .

$- \frac{\arcsin (n) (5 π)}{2} + \frac{a}{2} \cdot \cos (8 π) - (\frac{a}{2} + 1) \cos (0)$

Step 1.4

Move

$5$ to the left of

$\arcsin (n)$ .

$- \frac{5 \cdot \arcsin (n) π}{2} + \frac{a}{2} \cdot \cos (8 π) - (\frac{a}{2} + 1) \cos (0)$

Step 1.5

Subtract full rotations of

$2 π$ until the angle is greater than or equal to

$0$ and less than

$2 π$ .

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} \cdot \cos (0) - (\frac{a}{2} + 1) \cos (0)$

Step 1.6

The exact value of

$\cos (0)$ is

$1$ .

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} \cdot 1 - (\frac{a}{2} + 1) \cos (0)$

Step 1.7

Multiply

$\frac{a}{2}$ by

$1$ .

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} - (\frac{a}{2} + 1) \cos (0)$

Step 1.8

Apply the distributive property.

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} + (- \frac{a}{2} - 1 \cdot 1) \cos (0)$

Step 1.9

Multiply

$- 1$ by

$1$ .

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} + (- \frac{a}{2} - 1) \cos (0)$

Step 1.10

The exact value of

$\cos (0)$ is

$1$ .

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} + (- \frac{a}{2} - 1) \cdot 1$

Step 1.11

Multiply

$- \frac{a}{2} - 1$ by

$1$ .

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} - \frac{a}{2} - 1$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in

$- \frac{5 \arcsin (n) π}{2} + \frac{a}{2} - \frac{a}{2} - 1$ .

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Step 2.1.1

Subtract

$\frac{a}{2}$ from

$\frac{a}{2}$ .

$- \frac{5 \arcsin (n) π}{2} + 0 - 1$

Step 2.1.2

Add

$- \frac{5 \arcsin (n) π}{2}$ and

$0$ .

$- \frac{5 \arcsin (n) π}{2} - 1$

Step 2.2

Reorder factors in

$- \frac{5 \arcsin (n) π}{2} - 1$ .

$- \frac{5 π \arcsin (n)}{2} - 1$