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受欢迎的三角函数 >

solvefor y,sin(x)=x(1+tan(y))

解答

求解

y, sin (x) = x (1 + tan (y))

解答

y = arctan (\frac{sin ( x )}{x} - 1) + πn

求解步骤

sin (x) = x (1 + tan (y))

交换两边

x (1 + tan (y)) = sin (x)

两边除以

x; x \neq = 0

x (1 + tan (y)) = sin (x)

两边除以

x; x \neq = 0

\frac{x ( 1 + tan ( y ) )}{x} = \frac{sin ( x )}{x}; x \neq = 0

化简

1 + tan (y) = \frac{sin ( x )}{x}; x \neq = 0

1 + tan (y) = \frac{sin ( x )}{x}; x \neq = 0

将

1

到右边

1 + tan (y) = \frac{sin ( x )}{x}; x \neq = 0

两边减去

1

1 + tan (y) - 1 = \frac{sin ( x )}{x} - 1; x \neq = 0

化简

tan (y) = \frac{sin ( x )}{x} - 1; x \neq = 0

tan (y) = \frac{sin ( x )}{x} - 1; x \neq = 0

使用反三角函数性质

tan (y) = \frac{sin ( x )}{x} - 1

tan (y) = \frac{sin ( x )}{x} - 1

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

y = arctan (\frac{sin ( x )}{x} - 1) + πn

y = arctan (\frac{sin ( x )}{x} - 1) + πn

作图

流行的例子

sin(2x)-sin(x)=0,(0,2pi)

sin (2 x) - sin (x) = 0, (0, 2 π)

sin^4(x)+cos^4(x)= 7/9

sin^{4} (x) + cos^{4} (x) = \frac{7}{9}

tan(θ/5)+sqrt(3)=0

tan (\frac{θ}{5}) + 3 = 0

3tan(x)-sqrt(3)=0,0<= x<2pi

3 tan (x) - 3 = 0, 0 \leq x < 2 π

sec^{2} (θ) = 2