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受欢迎的三角函数 >

4cos(x+70)=3

解答

4 cos (x + 7 0^{\circ}) = 3

解答

x = 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}

+1

弧度

x = 0.72273 \dots - \frac{7 π}{18} + 2 πn, x = 2 π - 0.72273 \dots - \frac{7 π}{18} + 2 πn

求解步骤

4 cos (x + 7 0^{\circ}) = 3

两边除以

4

4 cos (x + 7 0^{\circ}) = 3

两边除以

4

\frac{4 cos ( x + 7 0 ^{\circ} )}{4} = \frac{3}{4}

化简

cos (x + 7 0^{\circ}) = \frac{3}{4}

cos (x + 7 0^{\circ}) = \frac{3}{4}

使用反三角函数性质

cos (x + 7 0^{\circ}) = \frac{3}{4}

cos (x + 7 0^{\circ}) = \frac{3}{4}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

解

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n : x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

将

7 0^{\circ}

到右边

x + 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

两边减去

7 0^{\circ}

x + 7 0^{\circ} - 7 0^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

化简

x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

解

x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

将

7 0^{\circ}

到右边

x + 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

两边减去

7 0^{\circ}

x + 7 0^{\circ} - 7 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

化简

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n - 7 0^{\circ}

以小数形式表示解

x = 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n - 7 0^{\circ}

作图

流行的例子

4 cos (2 x) = 0

tan(3x)=-(sqrt(3))/3

tan (3 x) = - \frac{3}{3}

tan^2(x)+3=2sec^2(x)

tan^{2} (x) + 3 = 2 sec^{2} (x)

8 sin^{2} (θ) - 2 = 0

4sin(2x)sin(x)=4cos(x)

4 sin (2 x) sin (x) = 4 cos (x)