Basic Math Examples

1200 \cdot cos (90) + 500 \cdot cos (30) + 1500 \cdot cos (180) + 2200 \cdot cos (200)

$1200 \cdot \cos (90) + 500 \cdot \cos (30) + 1500 \cdot \cos (180) + 2200 \cdot \cos (200)$

Step 1

Simplify each term.

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Step 1.1

The exact value of

$\cos (90)$ is

$0$ .

$1200 \cdot 0 + 500 \cdot \cos (30) + 1500 \cdot \cos (180) + 2200 \cdot \cos (200)$

Step 1.2

Multiply

$1200$ by

$0$ .

$0 + 500 \cdot \cos (30) + 1500 \cdot \cos (180) + 2200 \cdot \cos (200)$

Step 1.3

The exact value of

$\cos (30)$ is

$\frac{\sqrt{3}}{2}$ .

$0 + 500 \cdot \frac{\sqrt{3}}{2} + 1500 \cdot \cos (180) + 2200 \cdot \cos (200)$

Step 1.4

Cancel the common factor of

$2$ .

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Step 1.4.1

Factor

$2$ out of

$500$ .

$0 + 2 (250) \cdot \frac{\sqrt{3}}{2} + 1500 \cdot \cos (180) + 2200 \cdot \cos (200)$

Step 1.4.2

Cancel the common factor.

$0 + 2 \cdot 250 \cdot \frac{\sqrt{3}}{2} + 1500 \cdot \cos (180) + 2200 \cdot \cos (200)$

Step 1.4.3

Rewrite the expression.

$0 + 250 \cdot \sqrt{3} + 1500 \cdot \cos (180) + 2200 \cdot \cos (200)$

Step 1.5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$0 + 250 \sqrt{3} + 1500 \cdot (- \cos (0)) + 2200 \cdot \cos (200)$

Step 1.6

The exact value of

$\cos (0)$ is

$1$ .

$0 + 250 \sqrt{3} + 1500 \cdot (- 1 \cdot 1) + 2200 \cdot \cos (200)$

Step 1.7

Multiply

$1500 (- 1 \cdot 1)$ .

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Step 1.7.1

Multiply

$- 1$ by

$1$ .

$0 + 250 \sqrt{3} + 1500 \cdot - 1 + 2200 \cdot \cos (200)$

Step 1.7.2

Multiply

$1500$ by

$- 1$ .

$0 + 250 \sqrt{3} - 1500 + 2200 \cdot \cos (200)$

Step 1.8

Evaluate

$\cos (200)$ .

$0 + 250 \sqrt{3} - 1500 + 2200 \cdot - 0.93969262$

Step 1.9

Multiply

$2200$ by

$- 0.93969262$ .

$0 + 250 \sqrt{3} - 1500 - 2067.32376572$

Step 2

Simplify by subtracting numbers.

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Step 2.1

Add

$0$ and

$250 \sqrt{3}$ .

$250 \sqrt{3} - 1500 - 2067.32376572$

Step 2.2

Subtract

$2067.32376572$ from

$- 1500$ .

$250 \sqrt{3} - 3567.32376572$

Step 3

The result can be shown in multiple forms.

Exact Form:

$250 \sqrt{3} - 3567.32376572$

Decimal Form:

$- 3134.31106383 \dots$