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受欢迎的三角函数 >

sin(2x)= 2/5

解答

sin (2 x) = \frac{2}{5}

解答

x = \frac{0.41151 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.41151 \dots}{2} + πn

+1

度数

x = 11.78908 \dots^{\circ} + 18 0^{\circ} n, x = 78.21091 \dots^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x) = \frac{2}{5}

使用反三角函数性质

sin (2 x) = \frac{2}{5}

sin (2 x) = \frac{2}{5}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 x = arcsin (\frac{2}{5}) + 2 πn, 2 x = π - arcsin (\frac{2}{5}) + 2 πn

2 x = arcsin (\frac{2}{5}) + 2 πn, 2 x = π - arcsin (\frac{2}{5}) + 2 πn

解

2 x = arcsin (\frac{2}{5}) + 2 πn : x = \frac{arcsin ( \frac{2}{5} )}{2} + πn

2 x = arcsin (\frac{2}{5}) + 2 πn

两边除以

2

2 x = arcsin (\frac{2}{5}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( \frac{2}{5} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arcsin ( \frac{2}{5} )}{2} + πn

x = \frac{arcsin ( \frac{2}{5} )}{2} + πn

解

2 x = π - arcsin (\frac{2}{5}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{2}{5} )}{2} + πn

2 x = π - arcsin (\frac{2}{5}) + 2 πn

两边除以

2

2 x = π - arcsin (\frac{2}{5}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{2}{5} )}{2} + \frac{2 πn}{2}

化简

x = \frac{π}{2} - \frac{arcsin ( \frac{2}{5} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{2}{5} )}{2} + πn

x = \frac{arcsin ( \frac{2}{5} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{2}{5} )}{2} + πn

以小数形式表示解

x = \frac{0.41151 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.41151 \dots}{2} + πn

作图

流行的例子

sin(2x)+cos(x)=0,0<= x<= 2pi

sin (2 x) + cos (x) = 0, 0 \leq x \leq 2 π

cos (θ) = - 0.5

sec (x) = \frac{5}{3}

solvefor x,y=(sec(x))/(cos^1(x))+8y^2

so l v e f or x, y = \frac{sec ( x )}{cos ^{1} ( x )} + 8 y^{2}

sin(2x)sin(x)=0

sin (2 x) sin (x) = 0