15*sin(12*x)-10*sin(7*x)-10*sin(5*x)=0

asked by guest
on Mar 30, 2025 at 12:57 am



You asked:

Solve the equation 15sin⁡(12x)−10sin⁡(7x)−10sin⁡(5x)=015 \sin\left( 12 x \right) - 10 \sin\left( 7 x \right) - 10 \sin\left( 5 x \right) = 0 for the variable xx.

MathBot Answer:

x∈{2nπ  |  n∈Z}∪{π(2n+1)  |  n∈Z}∪{π(4n+3)2  |  n∈Z}∪{π(4n+1)2  |  n∈Z}∪{2π(3n+1)3  |  n∈Z}∪{2π(3n+2)3  |  n∈Z}∪{π(6n+5)3  |  n∈Z}∪{π(6n+1)3  |  n∈Z}∪{π(12n+11)6  |  n∈Z}∪{π(12n+5)6  |  n∈Z}∪{π(12n+7)6  |  n∈Z}∪{π(12n+1)6  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,6))  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,7))  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,8))  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,9))  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,10))  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,11))  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,0))+2π  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,1))+2π  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,2))+2π  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,3))+2π  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,4))+2π  |  n∈Z}∪{2nπ+2arctan⁡(CRootOf⁡(5x12−190x10+1495x8−2772x6+1475x4−206x2+1,5))+2π  |  n∈Z}x \in \left\{2 n \pi\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\pi \left(2 n + 1\right)\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(4 n + 3\right)}{2}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(4 n + 1\right)}{2}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{2 \pi \left(3 n + 1\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{2 \pi \left(3 n + 2\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(6 n + 5\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(6 n + 1\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(12 n + 11\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(12 n + 5\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(12 n + 7\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{\frac{\pi \left(12 n + 1\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 6\right)} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 7\right)} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 8\right)} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 9\right)} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 10\right)} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 11\right)} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 0\right)} \right)} + 2 \pi\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 1\right)} \right)} + 2 \pi\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 2\right)} \right)} + 2 \pi\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 3\right)} \right)} + 2 \pi\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 4\right)} \right)} + 2 \pi\; \middle|\; n \in \mathbb{Z}\right\} \cup \left\{2 n \pi + 2 \arctan{\left(\operatorname{CRootOf} {\left(5 x^{12} - 190 x^{10} + 1495 x^{8} - 2772 x^{6} + 1475 x^{4} - 206 x^{2} + 1, 5\right)} \right)} + 2 \pi\; \middle|\; n \in \mathbb{Z}\right\}

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