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受欢迎的三角函数 >

4cos(x)+3cos(x)=5

解答

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

解答

x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

+1

度数

x = 44.41530 \dots^{\circ} + 36 0^{\circ} n, x = 315.58469 \dots^{\circ} + 36 0^{\circ} n

求解步骤

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

化简

4 cos (x) + 3 cos (x) : 7 cos (x)

4 cos (x) + 3 cos (x)

同类项相加:

4 cos (x) + 3 cos (x) = 7 cos (x)

= 7 cos (x)

7 cos (x) = 5

两边除以

7

7 cos (x) = 5

两边除以

7

\frac{7 cos ( x )}{7} = \frac{5}{7}

化简

cos (x) = \frac{5}{7}

cos (x) = \frac{5}{7}

使用反三角函数性质

cos (x) = \frac{5}{7}

cos (x) = \frac{5}{7}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

x = arccos (\frac{5}{7}) + 2 πn, x = 2 π - arccos (\frac{5}{7}) + 2 πn

以小数形式表示解

x = 0.77519 \dots + 2 πn, x = 2 π - 0.77519 \dots + 2 πn

作图

流行的例子

4sin(2x)tan(x)-tan(x)=0

4 sin (2 x) tan (x) - tan (x) = 0

3sin(x)=sqrt(3)*sin(x)+3cos(x)+3sin(x)

3 sin (x) = 3 \cdot sin (x) + 3 cos (x) + 3 sin (x)

csc(θ)+1=0,(0,2pi)

csc (θ) + 1 = 0, (0, 2 π)

solvefor x,y^2=-2tan(2x)

so l v e f or x, y^{2} = - 2 tan (2 x)

2cos^2(a)-3cos(a)+1=0

2 cos^{2} (a) - 3 cos (a) + 1 = 0