Solve 180-978*sin10/978*cos10

$$\frac { 180 - 978 \cdot \sin 10 } { 978 \cdot \cos 10 }$$

Evaluate

$$\frac{169534704029035621}{16052366374098990400}\approx 0.010561353$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{180 - 978 \cdot 0.17364817766693033}{978 \cdot 0.984807753012208}$$

Multiply 978 and 0.17364817766693033 to get 169.82791775825786274.

$$\frac{180-169.82791775825786274}{978\times 0.984807753012208}$$

Subtract 169.82791775825786274 from 180 to get 10.17208224174213726.

$$\frac{10.17208224174213726}{978\times 0.984807753012208}$$

Multiply 978 and 0.984807753012208 to get 963.141982445939424.

$$\frac{10.17208224174213726}{963.141982445939424}$$

Expand \frac{10.17208224174213726}{963.141982445939424} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{1017208224174213726}{96314198244593942400}$$

Reduce the fraction \frac{1017208224174213726}{96314198244593942400} to lowest terms by extracting and canceling out 6.

$$\frac{169534704029035621}{16052366374098990400}$$

Factor

$$\frac{809 \cdot 209560820802269}{163 \cdot 443 \cdot 2399 \cdot 57915859 \cdot 2 ^ {6} \cdot 5 ^ {2}} = 0.010561352767439032$$