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受欢迎的三角函数 >

sin^2(x)+cos^2(x)+cos(x)=2

解答

sin^{2} (x) + cos^{2} (x) + cos (x) = 2

解答

x = 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n

求解步骤

sin^{2} (x) + cos^{2} (x) + cos (x) = 2

使用三角恒等式改写

sin^{2} (x) + cos^{2} (x) + cos (x)

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

= cos (x) + 1

cos (x) + 1 = 2

将

1

到右边

cos (x) + 1 = 2

两边减去

1

cos (x) + 1 - 1 = 2 - 1

化简

cos (x) = 1

cos (x) = 1

cos (x) = 1

的通解

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

作图

流行的例子

(sin^3(x))/(sin(x))=0

\frac{sin ^{3} ( x )}{sin ( x )} = 0

sin(135-x)=sin(x)

sin (135 - x) = sin (x)

tan (x) - 4 = - 1

4cos^2(x)-8cos(x)+3=0

4 cos^{2} (x) - 8 cos (x) + 3 = 0

sin (2 x) = - 0.6