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受欢迎的三角函数 >

5cos(x)+sqrt(2)=3cos(x),0<= x<= 2pi

解答

5 cos (x) + 2 = 3 cos (x), 0 \leq x \leq 2 π

解答

x = \frac{3 π}{4}, x = \frac{5 π}{4}

+1

度数

x = 13 5^{\circ}, x = 22 5^{\circ}

求解步骤

5 cos (x) + 2 = 3 cos (x), 0 \leq x \leq 2 π

用替代法求解

5 cos (x) + 2 = 3 cos (x)

令

: cos (x) = u

5 u + 2 = 3 u

5 u + 2 = 3 u : u = - \frac{2}{2}

5 u + 2 = 3 u

将

2

到右边

5 u + 2 = 3 u

两边减去

2

5 u + 2 - 2 = 3 u - 2

化简

5 u = 3 u - 2

5 u = 3 u - 2

将

3 u

para o lado esquerdo

5 u = 3 u - 2

两边减去

3 u

5 u - 3 u = 3 u - 2 - 3 u

化简

2 u = - 2

2 u = - 2

两边除以

2

2 u = - 2

两边除以

2

\frac{2 u}{2} = \frac{- 2}{2}

化简

u = - \frac{2}{2}

u = - \frac{2}{2}

u = cos (x)

代回

cos (x) = - \frac{2}{2}

cos (x) = - \frac{2}{2}

cos (x) = - \frac{2}{2}, 0 \leq x \leq 2 π : x = \frac{3 π}{4}, x = \frac{5 π}{4}

cos (x) = - \frac{2}{2}, 0 \leq x \leq 2 π

cos (x) = - \frac{2}{2}

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 = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{3 π}{4}, x = \frac{5 π}{4}

合并所有解

x = \frac{3 π}{4}, x = \frac{5 π}{4}

作图

流行的例子

2tan(2x+10)=-5.5

(sqrt(3))/3 =-1/3*tan(θ)

tan(x+pi/3)=sqrt(3)

-9sin^2(x)-5cos(x)+5=0