Trigonometry Examples

$\frac{25000 \cdot 9.8 + 0.8 \sin (x)}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Factor $0.16$ out of $25000 \cdot 9.8 + 0.8 \sin (x)$ .

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Step 1.1.1.1

Factor $0.16$ out of $25000 \cdot 9.8$ .

$\frac{0.16 (156250 \cdot 9.8) + 0.8 \sin (x)}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1.1.1.2

Factor $0.16$ out of $0.8 \sin (x)$ .

$\frac{0.16 (156250 \cdot 9.8) + 0.16 (5 \sin (x))}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1.1.1.3

Factor $0.16$ out of $0.16 (156250 \cdot 9.8) + 0.16 (5 \sin (x))$ .

$\frac{0.16 (156250 \cdot 9.8 + 5 \sin (x))}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1.1.2

Multiply $156250$ by $9.8$ .

$\frac{0.16 (1531250 + 5 \sin (x))}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1.1.3

Factor $5$ out of $1531250 + 5 \sin (x)$ .

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Step 1.1.3.1

Factor $5$ out of $1531250$ .

$\frac{0.16 (5 \cdot 306250 + 5 \sin (x))}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1.1.3.2

Factor $5$ out of $5 \cdot 306250 + 5 \sin (x)$ .

$\frac{0.16 (5 (306250 + \sin (x)))}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

$\frac{0.16 \cdot 5 (306250 + \sin (x))}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1.1.4

Multiply $0.16$ by $5$ .

$\frac{0.8 (306250 + \sin (x))}{\cos (x)} \cdot \sin (x) + 0.8 \cos (x) = 237369.4231$

Step 1.2

Combine $\frac{0.8 (306250 + \sin (x))}{\cos (x)}$ and $\sin (x)$ .

$\frac{0.8 (306250 + \sin (x)) \sin (x)}{\cos (x)} + 0.8 \cos (x) = 237369.4231$

Step 1.3

Separate fractions.

$\frac{0.8 (306250 + \sin (x))}{1} \cdot \frac{\sin (x)}{\cos (x)} + 0.8 \cos (x) = 237369.4231$

Step 1.4

Convert from $\frac{\sin (x)}{\cos (x)}$ to $\tan (x)$ .

$\frac{0.8 (306250 + \sin (x))}{1} \tan (x) + 0.8 \cos (x) = 237369.4231$

Step 1.5

Divide $0.8 (306250 + \sin (x))$ by $1$ .

$0.8 (306250 + \sin (x)) \tan (x) + 0.8 \cos (x) = 237369.4231$

Step 1.6

Apply the distributive property.

$(0.8 \cdot 306250 + 0.8 \sin (x)) \tan (x) + 0.8 \cos (x) = 237369.4231$

Step 1.7

Multiply $0.8$ by $306250$ .

$(245000 + 0.8 \sin (x)) \tan (x) + 0.8 \cos (x) = 237369.4231$

Step 1.8

Apply the distributive property.

$245000 \tan (x) + 0.8 \sin (x) \tan (x) + 0.8 \cos (x) = 237369.4231$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 0.76957818, - 2.37200977, 3.91117553, - 5.51360711, 7.05276349, - 8.65519508, 10.19436084$

Step 3