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受欢迎的三角函数 >

(sin(-20))/(cos(380))+tan(200)

解答

\frac{sin ( - 2 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )} + tan (20 0^{\circ})

解答

0

求解步骤

\frac{sin ( - 2 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )} + tan (20 0^{\circ})

化简

= \frac{sin ( - 2 0 ^{\circ} ) + tan ( 20 0 ^{\circ} ) cos ( 38 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

利用以下特性:

sin (- x) = - sin (x)

sin (- 2 0^{\circ}) = - sin (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 20 0 ^{\circ} ) cos ( 38 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

tan (20 0^{\circ}) = tan (2 0^{\circ})

tan (20 0^{\circ})

将

20 0^{\circ}

改写为

18 0^{\circ} + 2 0^{\circ}

= tan (18 0^{\circ} + 2 0^{\circ})

使用周期

tan

:

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 2 0^{\circ}) = tan (2 0^{\circ})

= tan (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 2 0 ^{\circ} ) cos ( 38 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

cos (38 0^{\circ}) = cos (2 0^{\circ})

cos (38 0^{\circ})

将

38 0^{\circ}

改写为

36 0^{\circ} + 2 0^{\circ}

= cos (36 0^{\circ} + 2 0^{\circ})

使用周期

cos

:

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 2 0^{\circ}) = cos (2 0^{\circ})

= cos (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 2 0 ^{\circ} ) cos ( 2 0 ^{\circ} )}{cos ( 38 0 ^{\circ} )}

cos (38 0^{\circ}) = cos (2 0^{\circ})

cos (38 0^{\circ})

将

38 0^{\circ}

改写为

36 0^{\circ} + 2 0^{\circ}

= cos (36 0^{\circ} + 2 0^{\circ})

使用周期

cos

:

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 2 0^{\circ}) = cos (2 0^{\circ})

= cos (2 0^{\circ})

= \frac{- sin ( 2 0 ^{\circ} ) + tan ( 2 0 ^{\circ} ) cos ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

使用三角恒等式改写:

tan (2 0^{\circ}) = \frac{sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

tan (2 0^{\circ})

使用基本三角恒等式:

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

= \frac{sin ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

= \frac{- sin ( 2 0 ^{\circ} ) + \frac{s i n ( 2 0 ^{\circ} )}{c o s ( 2 0 ^{\circ} )} cos ( 2 0 ^{\circ} )}{cos ( 2 0 ^{\circ} )}

化简

= 0

流行的例子

cot (- \frac{4 π}{3})

cos (0.3)

arctan (\frac{5}{1})

tan (\frac{π}{3} + \frac{π}{4})

sin (3 0^{\circ} + 4 5^{\circ})