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受欢迎的三角函数 >

sin(x)= 1/(sec(x))

解答

sin (x) = \frac{1}{sec ( x )}

解答

x = \frac{π}{4} + πn

+1

度数

x = 4 5^{\circ} + 18 0^{\circ} n

求解步骤

sin (x) = \frac{1}{sec ( x )}

两边减去

\frac{1}{sec ( x )}

sin (x) - \frac{1}{sec ( x )} = 0

化简

sin (x) - \frac{1}{sec ( x )} : \frac{sin ( x ) sec ( x ) - 1}{sec ( x )}

sin (x) - \frac{1}{sec ( x )}

将项转换为分式:

sin (x) = \frac{sin ( x ) sec ( x )}{sec ( x )}

= \frac{sin ( x ) sec ( x )}{sec ( x )} - \frac{1}{sec ( x )}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{sin ( x ) sec ( x ) - 1}{sec ( x )}

\frac{sin ( x ) sec ( x ) - 1}{sec ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

sin (x) sec (x) - 1 = 0

使用三角恒等式改写

sin (x) sec (x) - 1

sec (x) sin (x) = tan (x)

sec (x) sin (x)

用 sin, cos 表示

sec (x) sin (x)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} sin (x)

化简

\frac{1}{cos ( x )} sin (x) : \frac{sin ( x )}{cos ( x )}

\frac{1}{cos ( x )} sin (x)

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 sin ( x )}{cos ( x )}

乘以:

1 \cdot sin (x) = sin (x)

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )}

= \frac{sin ( x )}{cos ( x )}

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x)

= - 1 + tan (x)

- 1 + tan (x) = 0

将

1

到右边

- 1 + tan (x) = 0

两边加上

1

- 1 + tan (x) + 1 = 0 + 1

化简

tan (x) = 1

tan (x) = 1

tan (x) = 1

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

作图

流行的例子

cos (12 x) = 0

sin (α) = - \frac{3}{5}

solvefor x,y= 1/pi arctan(x/s)+1/2

so l v e f or x, y = \frac{1}{π} arctan (\frac{x}{s}) + \frac{1}{2}

8sin(2x)=16cos(x)

8 sin (2 x) = 16 cos (x)

3 arccos (x) = π