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受欢迎的三角函数 >

sin(θ)=(-2)/(2sqrt(2)),0<= θ<2pi

解答

sin (θ) = \frac{- 2}{2 2}, 0 \leq θ < 2 π

解答

θ = \frac{5 π}{4}, θ = \frac{7 π}{4}

求解步骤

sin (θ) = \frac{- 2}{2 2}, 0 \leq θ < 2 π

化简

\frac{- 2}{2 2} : - \frac{2}{2}

\frac{- 2}{2 2}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{2 2}

数字相除:

\frac{2}{2} = 1

= - \frac{1}{2}

- \frac{1}{2}

有理化:

- \frac{2}{2}

- \frac{1}{2}

乘以共轭根式

\frac{2}{2}

= - \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

使用根式运算法则:

a a = a

22 = 2

= 2

= - \frac{2}{2}

= - \frac{2}{2}

sin (θ) = - \frac{2}{2}

sin (θ) = - \frac{2}{2}

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

θ = \frac{5 π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

在

0 \leq θ < 2 π

范围内的解

θ = \frac{5 π}{4}, θ = \frac{7 π}{4}

作图

流行的例子

(sin(θ)+1)(sin(θ)-1)=0

(30)/(sin(x))=(50)/(sin(90))

cos(θ)=(2sqrt(3))/5

cos(2x)(sin(x)+(sqrt(2))/2)=0