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受欢迎的三角函数 >

sin(θ)cot(θ)=(sqrt(3))/2

解答

sin (θ) cot (θ) = \frac{3}{2}

解答

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

+1

度数

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

sin (θ) cot (θ) = \frac{3}{2}

两边减去

\frac{3}{2}

sin (θ) cot (θ) - \frac{3}{2} = 0

化简

sin (θ) cot (θ) - \frac{3}{2} : \frac{2 sin ( θ ) cot ( θ ) - 3}{2}

sin (θ) cot (θ) - \frac{3}{2}

将项转换为分式:

sin (θ) cot (θ) = \frac{sin ( θ ) cot ( θ ) 2}{2}

= \frac{sin ( θ ) cot ( θ ) \cdot 2}{2} - \frac{3}{2}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{sin ( θ ) cot ( θ ) \cdot 2 - 3}{2}

\frac{2 sin ( θ ) cot ( θ ) - 3}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 sin (θ) cot (θ) - 3 = 0

使用三角恒等式改写

- 3 + 2 cot (θ) sin (θ)

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= - 3 + 2 \cdot \frac{cos ( θ )}{sin ( θ )} sin (θ)

2 \cdot \frac{cos ( θ )}{sin ( θ )} sin (θ) = 2 cos (θ)

2 \cdot \frac{cos ( θ )}{sin ( θ )} sin (θ)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( θ ) \cdot 2 sin ( θ )}{sin ( θ )}

约分:

sin (θ)

= cos (θ) \cdot 2

= - 3 + 2 cos (θ)

- 3 + 2 cos (θ) = 0

将

3

到右边

- 3 + 2 cos (θ) = 0

两边加上

3

- 3 + 2 cos (θ) + 3 = 0 + 3

化简

2 cos (θ) = 3

2 cos (θ) = 3

两边除以

2

2 cos (θ) = 3

两边除以

2

\frac{2 cos ( θ )}{2} = \frac{3}{2}

化简

cos (θ) = \frac{3}{2}

cos (θ) = \frac{3}{2}

cos (θ) = \frac{3}{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}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

作图

流行的例子

cos^2(θ)+(10^2)/(9.81(1))cos(θ)-1=0

cos^{2} (θ) + \frac{1 0 ^{2}}{9.81 ( 1 )} cos (θ) - 1 = 0

cos^{4} (x) = \frac{1}{16}

solvefor w,P=4(Y/(Psin(w)))

so l v e f or w, P = 4 (\frac{Y}{P sin ( w )})

tan(2θ)=(500)/(350-75)

tan (2 θ) = \frac{500}{350 - 75}

sec (a) = - 2