Solve cos 3x = 0.87 for 0 ≤ x ≤ 120

asked by guest
on Jan 24, 2025 at 9:25 am



MathBot Answer:

x=arctan(243187)3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3}, x=arctan(243187)3+2π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{2 \pi}{3}, x=arctan(243187)3+4π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{4 \pi}{3}, x=arctan(243187)3+2πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 2 \pi, x=arctan(243187)3+8π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{8 \pi}{3}, x=arctan(243187)3+10π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{10 \pi}{3}, x=arctan(243187)3+4πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 4 \pi, x=arctan(243187)3+14π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{14 \pi}{3}, x=arctan(243187)3+16π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{16 \pi}{3}, x=arctan(243187)3+6πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 6 \pi, x=arctan(243187)3+20π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{20 \pi}{3}, x=arctan(243187)3+22π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{22 \pi}{3}, x=arctan(243187)3+8πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 8 \pi, x=arctan(243187)3+26π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{26 \pi}{3}, x=arctan(243187)3+28π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{28 \pi}{3}, x=arctan(243187)3+10πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 10 \pi, x=arctan(243187)3+32π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{32 \pi}{3}, x=arctan(243187)3+34π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{34 \pi}{3}, x=arctan(243187)3+12πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 12 \pi, x=arctan(243187)3+38π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{38 \pi}{3}, x=arctan(243187)3+40π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{40 \pi}{3}, x=arctan(243187)3+14πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 14 \pi, x=arctan(243187)3+44π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{44 \pi}{3}, x=arctan(243187)3+46π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{46 \pi}{3}, x=arctan(243187)3+16πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 16 \pi, x=arctan(243187)3+50π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{50 \pi}{3}, x=arctan(243187)3+52π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{52 \pi}{3}, x=arctan(243187)3+18πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 18 \pi, x=arctan(243187)3+56π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{56 \pi}{3}, x=arctan(243187)3+58π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{58 \pi}{3}, x=arctan(243187)3+20πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 20 \pi, x=arctan(243187)3+62π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{62 \pi}{3}, x=arctan(243187)3+64π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{64 \pi}{3}, x=arctan(243187)3+22πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 22 \pi, x=arctan(243187)3+68π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{68 \pi}{3}, x=arctan(243187)3+70π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{70 \pi}{3}, x=arctan(243187)3+24πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 24 \pi, x=arctan(243187)3+74π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{74 \pi}{3}, x=arctan(243187)3+76π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{76 \pi}{3}, x=arctan(243187)3+26πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 26 \pi, x=arctan(243187)3+80π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{80 \pi}{3}, x=arctan(243187)3+82π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{82 \pi}{3}, x=arctan(243187)3+28πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 28 \pi, x=arctan(243187)3+86π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{86 \pi}{3}, x=arctan(243187)3+88π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{88 \pi}{3}, x=arctan(243187)3+30πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 30 \pi, x=arctan(243187)3+92π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{92 \pi}{3}, x=arctan(243187)3+94π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{94 \pi}{3}, x=arctan(243187)3+32πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 32 \pi, x=arctan(243187)3+98π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{98 \pi}{3}, x=arctan(243187)3+100π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{100 \pi}{3}, x=arctan(243187)3+34πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 34 \pi, x=arctan(243187)3+104π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{104 \pi}{3}, x=arctan(243187)3+106π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{106 \pi}{3}, x=arctan(243187)3+36πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 36 \pi, x=arctan(243187)3+110π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{110 \pi}{3}, x=arctan(243187)3+112π3x = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{112 \pi}{3}, x=arctan(243187)3+38πx = - \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 38 \pi, x=arctan(243187)3+2π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{2 \pi}{3}, x=arctan(243187)3+4π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{4 \pi}{3}, x=arctan(243187)3+2πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 2 \pi, x=arctan(243187)3+8π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{8 \pi}{3}, x=arctan(243187)3+10π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{10 \pi}{3}, x=arctan(243187)3+4πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 4 \pi, x=arctan(243187)3+14π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{14 \pi}{3}, x=arctan(243187)3+16π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{16 \pi}{3}, x=arctan(243187)3+6πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 6 \pi, x=arctan(243187)3+20π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{20 \pi}{3}, x=arctan(243187)3+22π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{22 \pi}{3}, x=arctan(243187)3+8πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 8 \pi, x=arctan(243187)3+26π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{26 \pi}{3}, x=arctan(243187)3+28π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{28 \pi}{3}, x=arctan(243187)3+10πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 10 \pi, x=arctan(243187)3+32π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{32 \pi}{3}, x=arctan(243187)3+34π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{34 \pi}{3}, x=arctan(243187)3+12πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 12 \pi, x=arctan(243187)3+38π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{38 \pi}{3}, x=arctan(243187)3+40π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{40 \pi}{3}, x=arctan(243187)3+14πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 14 \pi, x=arctan(243187)3+44π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{44 \pi}{3}, x=arctan(243187)3+46π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{46 \pi}{3}, x=arctan(243187)3+16πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 16 \pi, x=arctan(243187)3+50π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{50 \pi}{3}, x=arctan(243187)3+52π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{52 \pi}{3}, x=arctan(243187)3+18πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 18 \pi, x=arctan(243187)3+56π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{56 \pi}{3}, x=arctan(243187)3+58π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{58 \pi}{3}, x=arctan(243187)3+20πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 20 \pi, x=arctan(243187)3+62π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{62 \pi}{3}, x=arctan(243187)3+64π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{64 \pi}{3}, x=arctan(243187)3+22πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 22 \pi, x=arctan(243187)3+68π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{68 \pi}{3}, x=arctan(243187)3+70π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{70 \pi}{3}, x=arctan(243187)3+24πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 24 \pi, x=arctan(243187)3+74π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{74 \pi}{3}, x=arctan(243187)3+76π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{76 \pi}{3}, x=arctan(243187)3+26πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 26 \pi, x=arctan(243187)3+80π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{80 \pi}{3}, x=arctan(243187)3+82π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{82 \pi}{3}, x=arctan(243187)3+28πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 28 \pi, x=arctan(243187)3+86π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{86 \pi}{3}, x=arctan(243187)3+88π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{88 \pi}{3}, x=arctan(243187)3+30πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 30 \pi, x=arctan(243187)3+92π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{92 \pi}{3}, x=arctan(243187)3+94π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{94 \pi}{3}, x=arctan(243187)3+32πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 32 \pi, x=arctan(243187)3+98π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{98 \pi}{3}, x=arctan(243187)3+100π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{100 \pi}{3}, x=arctan(243187)3+34πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 34 \pi, x=arctan(243187)3+104π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{104 \pi}{3}, x=arctan(243187)3+106π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{106 \pi}{3}, x=arctan(243187)3+36πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 36 \pi, x=arctan(243187)3+110π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{110 \pi}{3}, x=arctan(243187)3+112π3x = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + \frac{112 \pi}{3}, x=arctan(243187)3+38πx = \frac{\arctan{\left(\frac{\sqrt{2431}}{87} \right)}}{3} + 38 \pi are the solutions to the equation cos(3x)=0.87\cos\left( 3 x \right) = 0.87 that satisfy the inequality 0x1200 \le x \le 120.