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受欢迎的三角函数 >

sec(3x)-4=0

解答

sec (3 x) - 4 = 0

解答

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = 25.17416 \dots^{\circ} + 12 0^{\circ} n, x = 94.82583 \dots^{\circ} + 12 0^{\circ} n

求解步骤

sec (3 x) - 4 = 0

将

4

到右边

sec (3 x) - 4 = 0

两边加上

4

sec (3 x) - 4 + 4 = 0 + 4

化简

sec (3 x) = 4

sec (3 x) = 4

使用反三角函数性质

sec (3 x) = 4

sec (3 x) = 4

的通解

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

3 x = arcsec (4) + 2 πn, 3 x = 2 π - arcsec (4) + 2 πn

3 x = arcsec (4) + 2 πn, 3 x = 2 π - arcsec (4) + 2 πn

解

3 x = arcsec (4) + 2 πn : x = \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

3 x = arcsec (4) + 2 πn

两边除以

3

3 x = arcsec (4) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

化简

x = \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

x = \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

解

3 x = 2 π - arcsec (4) + 2 πn : x = \frac{2 π}{3} - \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

3 x = 2 π - arcsec (4) + 2 πn

两边除以

3

3 x = 2 π - arcsec (4) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

化简

x = \frac{2 π}{3} - \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

x = \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arcsec ( 4 )}{3} + \frac{2 πn}{3}

以小数形式表示解

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

6sin^2(θ)+5sin(θ)=-2sin(θ)-1

6 sin^{2} (θ) + 5 sin (θ) = - 2 sin (θ) - 1

solvefor t,x=5cos(t)

so l v e f or t, x = 5 cos (t)

tan (θ) = \frac{π}{2}

49sin(2β)=25,tan(β)<0

49 sin (2 β) = 25, tan (β) < 0

cos (θ) = - 0.076