Solve cos^2(pi/9)+cos^2(2pi/9)+cos^2(3pi/9)+cos^2(4pi/9)

$$\cos ^ { 2 } ( \frac { \pi } { 9 } ) + \cos ^ { 2 } ( \frac { 2 \pi } { 9 } ) + \cos ^ { 2 } ( \frac { 3 \pi } { 9 } ) + \cos ^ { 2 } ( \frac { 4 \pi } { 9 } )$$

Evaluate

$$1.7499999999999999972718530894573281$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9396926207859084 ^ {2} + 0.766044443118978 ^ {2} + \cos^{2}(\frac{3 \pi}{9}) + 0.17364817766693041 ^ {2}$$

Calculate 0.9396926207859084 to the power of 2 and get 0.88302222155948904756966801319056.

$$0.88302222155948904756966801319056+0.766044443118978^{2}+\left(\cos(\frac{3\pi }{9})\right)^{2}+0.17364817766693041^{2}$$

Calculate 0.766044443118978 to the power of 2 and get 0.586824088833465120492663764484.

$$0.88302222155948904756966801319056+0.586824088833465120492663764484+\left(\cos(\frac{3\pi }{9})\right)^{2}+0.17364817766693041^{2}$$

Add 0.88302222155948904756966801319056 and 0.586824088833465120492663764484 to get 1.46984631039295416806233177767456.

$$1.46984631039295416806233177767456+\left(\cos(\frac{3\pi }{9})\right)^{2}+0.17364817766693041^{2}$$

Divide 3\pi by 9 to get \frac{1}{3}\pi .

$$1.46984631039295416806233177767456+\left(\cos(\frac{1}{3}\pi )\right)^{2}+0.17364817766693041^{2}$$

Get the value of \cos(\frac{1}{3}\pi ) from trigonometric values table.

$$1.46984631039295416806233177767456+\left(\frac{1}{2}\right)^{2}+0.17364817766693041^{2}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$1.46984631039295416806233177767456+\frac{1}{4}+0.17364817766693041^{2}$$

Add 1.46984631039295416806233177767456 and \frac{1}{4} to get \frac{5374519719977981775194786805233}{3125000000000000000000000000000}.

$$\frac{5374519719977981775194786805233}{3125000000000000000000000000000}+0.17364817766693041^{2}$$

Calculate 0.17364817766693041 to the power of 2 and get 0.0301536896070458292095213117827681.

$$\frac{5374519719977981775194786805233}{3125000000000000000000000000000}+0.0301536896070458292095213117827681$$

Add \frac{5374519719977981775194786805233}{3125000000000000000000000000000} and 0.0301536896070458292095213117827681 to get \frac{17499999999999999972718530894573281}{10000000000000000000000000000000000}.

$$\frac{17499999999999999972718530894573281}{10000000000000000000000000000000000}$$