Solve cos(12)θ+3cos(10)θ+3cos(8)θ+cos(6)θ+2cos(4)θ+2cos(2)θ-2

$$\cos ( 12 ) \theta +3 \cos ( 10 ) \theta +3 \cos ( 8 ) \theta + \cos ( 6 ) \theta +2 \cos ( 4 ) \theta +2 \cos ( 2 ) \theta -2$$

Evaluate

$$\frac{59459033579606271\theta }{5000000000000000}-2$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9781476007338057 \theta + 3 \cdot 0.984807753012208 \theta + 3 \cdot 0.9902680687415704 \theta + 0.9945218953682733 \theta + 2 \cdot 0.9975640502598242 \theta + 2 \cdot 0.9993908270190958 \theta - 2$$

Multiply 3 and 0.984807753012208 to get 2.954423259036624.

$$0.9781476007338057\theta +2.954423259036624\theta +3\times 0.9902680687415704\theta +0.9945218953682733\theta +2\times 0.9975640502598242\theta +2\times 0.9993908270190958\theta -2$$

Combine 0.9781476007338057\theta and 2.954423259036624\theta to get 3.9325708597704297\theta .

$$3.9325708597704297\theta +3\times 0.9902680687415704\theta +0.9945218953682733\theta +2\times 0.9975640502598242\theta +2\times 0.9993908270190958\theta -2$$

Multiply 3 and 0.9902680687415704 to get 2.9708042062247112.

$$3.9325708597704297\theta +2.9708042062247112\theta +0.9945218953682733\theta +2\times 0.9975640502598242\theta +2\times 0.9993908270190958\theta -2$$

Combine 3.9325708597704297\theta and 2.9708042062247112\theta to get 6.9033750659951409\theta .

$$6.9033750659951409\theta +0.9945218953682733\theta +2\times 0.9975640502598242\theta +2\times 0.9993908270190958\theta -2$$

Combine 6.9033750659951409\theta and 0.9945218953682733\theta to get 7.8978969613634142\theta .

$$7.8978969613634142\theta +2\times 0.9975640502598242\theta +2\times 0.9993908270190958\theta -2$$

Multiply 2 and 0.9975640502598242 to get 1.9951281005196484.

$$7.8978969613634142\theta +1.9951281005196484\theta +2\times 0.9993908270190958\theta -2$$

Combine 7.8978969613634142\theta and 1.9951281005196484\theta to get 9.8930250618830626\theta .

$$9.8930250618830626\theta +2\times 0.9993908270190958\theta -2$$

Multiply 2 and 0.9993908270190958 to get 1.9987816540381916.

$$9.8930250618830626\theta +1.9987816540381916\theta -2$$

Combine 9.8930250618830626\theta and 1.9987816540381916\theta to get 11.8918067159212542\theta .

$$11.8918067159212542\theta -2$$