Solve sin^233^circ+sin^257^circ

$$\sin ^ { 2 } 33 ^ { \circ } + \sin ^ { 2 } 57 ^ { \circ }$$

Evaluate

$$0.99999999999999980191645176442562$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.5446390350150271 ^ {2} + 0.8386705679454239 ^ {2}$$

Calculate 0.5446390350150271 to the power of 2 and get 0.29663167846209991548592281373441.

$$0.29663167846209991548592281373441+0.8386705679454239^{2}$$

Calculate 0.8386705679454239 to the power of 2 and get 0.70336832153789988643052895069121.

$$0.29663167846209991548592281373441+0.70336832153789988643052895069121$$

Add 0.29663167846209991548592281373441 and 0.70336832153789988643052895069121 to get 0.99999999999999980191645176442562.

$$0.99999999999999980191645176442562$$

Factor

$$\frac{41 \cdot 1219512195121950977946892395641}{2 ^ {31} \cdot 5 ^ {32}} = 0.9999999999999998$$