Solve ytan6^circ+11760/cos6^circ=x

$$y \tan 6 ^ { \circ } + \frac { 11760 } { \cos 6 ^ { \circ } } = x$$

Solve for x

$$x=\frac{5255211763283823y_{0}}{50000000000000000}+\frac{5600000000000000000}{473581854937273}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$y 0.10510423526567646 + \frac{11760}{0.9945218953682733} = x$$

Expand \frac{11760}{0.9945218953682733} by multiplying both numerator and the denominator by 10000000000000000.

$$y_{0}\times 0.10510423526567646+\frac{117600000000000000000}{9945218953682733}=x$$

Reduce the fraction \frac{117600000000000000000}{9945218953682733} to lowest terms by extracting and canceling out 21.

$$y_{0}\times 0.10510423526567646+\frac{5600000000000000000}{473581854937273}=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=y_{0}\times 0.10510423526567646+\frac{5600000000000000000}{473581854937273}$$

Solve for y_0

$$y_{0}=\frac{50000000000000000x}{5255211763283823}-\frac{280000000000000000000000000000000000}{2488772934944130119556160634679}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$y 0.10510423526567646 + \frac{11760}{0.9945218953682733} = x$$

Expand \frac{11760}{0.9945218953682733} by multiplying both numerator and the denominator by 10000000000000000.

$$y_{0}\times 0.10510423526567646+\frac{117600000000000000000}{9945218953682733}=x$$

Reduce the fraction \frac{117600000000000000000}{9945218953682733} to lowest terms by extracting and canceling out 21.

$$y_{0}\times 0.10510423526567646+\frac{5600000000000000000}{473581854937273}=x$$

Subtract \frac{5600000000000000000}{473581854937273} from both sides.

$$y_{0}\times 0.10510423526567646=x-\frac{5600000000000000000}{473581854937273}$$

The equation is in standard form.

$$0.10510423526567646y_{0}=x-\frac{5600000000000000000}{473581854937273}$$

Divide both sides of the equation by 0.10510423526567646, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.10510423526567646y_{0}}{0.10510423526567646}=\frac{x-\frac{5600000000000000000}{473581854937273}}{0.10510423526567646}$$

Dividing by 0.10510423526567646 undoes the multiplication by 0.10510423526567646.

$$y_{0}=\frac{x-\frac{5600000000000000000}{473581854937273}}{0.10510423526567646}$$

Divide x-\frac{5600000000000000000}{473581854937273} by 0.10510423526567646 by multiplying x-\frac{5600000000000000000}{473581854937273} by the reciprocal of 0.10510423526567646.

$$y_{0}=\frac{50000000000000000x}{5255211763283823}-\frac{280000000000000000000000000000000000}{2488772934944130119556160634679}$$