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第七課 課題:以反函數形式給定的弧底各三角函數的求法 檢查完了家庭作業以後,叫一个学生到黑板上求sin(arcsin x)和cos(arcsin x)。因为-(π/2)≤arcsin x≤π/2,而正弦在这个區間內是正數或0,所以在根号前应取十号;因而,与數x的符号無關,我們有: 叫另一个学生求弧arcsin x的正切和餘切:在这裏根号前取+号。事实上,若x<0,則也有tan(arcsinx)<0,而若x>0,則也有tan(arcsin x)>0;所以
Lesson 7 Topic: Solving the trigonometric functions of the arc base given in inverse function After checking homework, ask a student to find sin (arcsin x) and cos (arcsin x) on the blackboard. Since -(π/2) ≤ arcsin x ≤ π/2, and the sine is positive or 0 in this interval, the number should be taken before the root number; therefore, regardless of the sign of the number x, we have: A student asks for the tangent and cotangent of arcsin x: Take the + sign before the root number here. In fact, if x<0, there is also tan(arcsinx)<0, and if x>0, there is also tan(arcsin x)>0;