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正切函数的诱导公式

正切函数的诱导公式. 吕绍荣. 【 问题提出 】: 角 a 的正切值与角 2π+a ， 2π-a ， π-a ， π+a ， -a 之间的正切值有什么关系？. tan( 2π+a )=tana tan (-a)=-tana tan (2π-a) =-tana tan (π-a)=- tana tan (π+a) =tana tan(π/2-a) =cota tan(π/2+a) =-cota. 例一：. 化简： tan(-π+a)tan(3π-a)tan(-a-π)

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正切函数的诱导公式

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  1. 正切函数的诱导公式 吕绍荣

  2. 【问题提出】: 角a的正切值与角2π+a，2π-a， π-a，π+a，-a之间的正切值有什么关系？

  3. tan( 2π+a )=tanatan (-a)=-tanatan (2π-a) =-tana tan (π-a)=- tana tan (π+a) =tana tan(π/2-a) =cota tan(π/2+a) =-cota

  4. 例一： • 化简： tan(-π+a)tan(3π-a)tan(-a-π) tan (2π-a) tan(3π+a)

  5. 课堂练习： • 化简： • (1) p2tan(π/4)-q2sin(3π/2)+pqcosπ -pqtan(5π/4) • (2) sin(π-a)cos(3π-a)tan(a-2π) tan(4π-a)sin(5π+a)

  6. 例二： • 已知sin(π-a)=log80.25，且-π/2<a<0 试求tan(a+1.5π)的值.

  7. 相关练习： • 已知sin(π+a)=-1/3，0<a<π/3， 试求sin(a+1.5π)tan(a-2.5π)的值.

  8. 巩固联系： • (1)证明： tan (2π-a) sin(-2π-a)cos (6π-a) cos (a-π)sin (5π+a) =tana • (2)已知tan (π+a) =4，求 sin (2π-a) cos (2π-a) 的值。 • (3)教材P38.5 P39.7

  9. OVER

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