Solve 4cos20^circ+6cos75^circ+5cos40^circ

$$4 \cos 20 ^ { \circ } + 6 \cos 75 ^ { \circ } + 5 \cos 40 ^ { \circ }$$

Evaluate

$$9.14190696935364804$$

Solution Steps

Evaluate trigonometric functions in the problem

$$4 \cdot 0.9396926207859084 + 6 \cdot 0.25881904510252074 + 5 \cdot 0.766044443118978$$

Multiply 4 and 0.9396926207859084 to get 3.7587704831436336.

$$3.7587704831436336+6\times 0.25881904510252074+5\times 0.766044443118978$$

Multiply 6 and 0.25881904510252074 to get 1.55291427061512444.

$$3.7587704831436336+1.55291427061512444+5\times 0.766044443118978$$

Add 3.7587704831436336 and 1.55291427061512444 to get 5.31168475375875804.

$$5.31168475375875804+5\times 0.766044443118978$$

Multiply 5 and 0.766044443118978 to get 3.83022221559489.

$$5.31168475375875804+3.83022221559489$$

Add 5.31168475375875804 and 3.83022221559489 to get 9.14190696935364804.

$$9.14190696935364804$$

Factor

$$\frac{3 \cdot 67 \cdot 1137053105641001}{2 ^ {15} \cdot 5 ^ {17}} = 9\frac{3547674233841216}{25000000000000000} = 9.141906969353649$$