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受欢迎的三角函数 >

sec(θ)= 13/5 \land sin(θ)<0

解答

sec (θ) = \frac{13}{5} and sin (θ) < 0

解答

θ = 5.10718 \dots + 2 πn

+1

间隔符号

θ = 5.10718 \dots + 2 πn

求解步骤

sec (θ) = \frac{13}{5} and sin (θ) < 0

sec (θ) = \frac{13}{5} : θ = 1.17600 \dots + 2 πn, θ = 2 π - 1.17600 \dots + 2 πn

sec (θ) = \frac{13}{5}

使用反三角函数性质

sec (θ) = \frac{13}{5}

sec (θ) = \frac{13}{5}

的通解

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

θ = arcsec (\frac{13}{5}) + 2 πn, θ = 2 π - arcsec (\frac{13}{5}) + 2 πn

θ = arcsec (\frac{13}{5}) + 2 πn, θ = 2 π - arcsec (\frac{13}{5}) + 2 πn

以小数形式表示解

θ = 1.17600 \dots + 2 πn, θ = 2 π - 1.17600 \dots + 2 πn

sin (θ) < 0 : - π + 2 πn < θ < 2 πn

sin (θ) < 0

对于

sin (x) < a

，若

- 1 < a \leq 1

，则

- π - arcsin (a) + 2 πn < x < arcsin (a) + 2 πn

- π - arcsin (0) + 2 πn < θ < arcsin (0) + 2 πn

化简

- π - arcsin (0) : - π

- π - arcsin (0)

使用以下普通恒等式:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= - π - 0

- π - 0 = - π

= - π

化简

arcsin (0) : 0

arcsin (0)

使用以下普通恒等式:

arcsin (0) = 0

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= 0

- π + 2 πn < θ < 0 + 2 πn

化简

- π + 2 πn < θ < 2 πn

合并区间

(θ = 1.17600 \dots + 2 πn or θ = 2 π - 1.17600 \dots + 2 πn) and - π + 2 πn < θ < 2 πn

合并重叠的区间

θ = 5.10718 \dots + 2 πn

流行的例子

cot(θ)= 2/3 \land csc(θ)<0

cot (θ) = \frac{2}{3} and csc (θ) < 0

-(sqrt(3))/2 <cos(x)<(sqrt(3))/2

- \frac{3}{2} < cos (x) < \frac{3}{2}

0<=-cos(b)0.6428<= 180

0 \leq - cos (b) 0.6428 \leq 180

-sqrt(3)<tan(θ)<1

- 3 < tan (θ) < 1

-1/2 <cos(x)<= 1/2

- \frac{1}{2} < cos (x) \leq \frac{1}{2}