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受欢迎的三角函数 >

4sec(θ)-5=0

解答

4 sec (θ) - 5 = 0

解答

θ = 0.64350 \dots + 2 πn, θ = 2 π - 0.64350 \dots + 2 πn

+1

度数

θ = 36.86989 \dots^{\circ} + 36 0^{\circ} n, θ = 323.13010 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4 sec (θ) - 5 = 0

将

5

到右边

4 sec (θ) - 5 = 0

两边加上

5

4 sec (θ) - 5 + 5 = 0 + 5

化简

4 sec (θ) = 5

4 sec (θ) = 5

两边除以

4

4 sec (θ) = 5

两边除以

4

\frac{4 sec ( θ )}{4} = \frac{5}{4}

化简

sec (θ) = \frac{5}{4}

sec (θ) = \frac{5}{4}

使用反三角函数性质

sec (θ) = \frac{5}{4}

sec (θ) = \frac{5}{4}

的通解

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

θ = arcsec (\frac{5}{4}) + 2 πn, θ = 2 π - arcsec (\frac{5}{4}) + 2 πn

θ = arcsec (\frac{5}{4}) + 2 πn, θ = 2 π - arcsec (\frac{5}{4}) + 2 πn

以小数形式表示解

θ = 0.64350 \dots + 2 πn, θ = 2 π - 0.64350 \dots + 2 πn

作图

流行的例子

3sin(x)+5cos(x)=0

3 sin (x) + 5 cos (x) = 0

sec (3 x) = - 2

tan(x)-2cot(x)=1

tan (x) - 2 cot (x) = 1

sqrt(2)cos(2θ)=-1

2 cos (2 θ) = - 1

16 cos^{2} (x) = 12