Solve 580*sin38^circ+72/580*cos38^circ

$$\frac { 580 \times \sin 38 ^ { \circ } + 72 } { 580 \times \cos 38 ^ { \circ } }$$

Evaluate

$$\frac{107270913922220439}{114261559272974690}\approx 0.938818922$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{580 \cdot 0.6156614753256582 + 72}{580 \cdot 0.788010753606722}$$

Multiply 580 and 0.6156614753256582 to get 357.083655688881756.

$$\frac{357.083655688881756+72}{580\times 0.788010753606722}$$

Add 357.083655688881756 and 72 to get 429.083655688881756.

$$\frac{429.083655688881756}{580\times 0.788010753606722}$$

Multiply 580 and 0.788010753606722 to get 457.04623709189876.

$$\frac{429.083655688881756}{457.04623709189876}$$

Expand \frac{429.083655688881756}{457.04623709189876} by multiplying both numerator and the denominator by 1000000000000000.

$$\frac{429083655688881756}{457046237091898760}$$

Reduce the fraction \frac{429083655688881756}{457046237091898760} to lowest terms by extracting and canceling out 4.

$$\frac{107270913922220439}{114261559272974690}$$

Factor

$$\frac{3727 \cdot 3198011922673 \cdot 3 ^ {2}}{2 \cdot 5 \cdot 29 \cdot 394005376803361} = 0.9388189221708996$$