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本文拟从反三角函数性质的讨论入手,通过分析一些错例,介绍反三角函数学习中的五点注意。 1。注意主值区间用反三角函数表示角或求值时。应注意反三角函数的主值区间。例1 若sinx=(3~(1/2))/5,x∈(π/2,π),试用反正弦函数表示。错解 x=arcsin(3~(1/2))/5 [错因分析] arcsin(3~(1/2))/5∈(v,π/2),而x∈《π/2,π)。故上述解答不对。正解∵x∈(π/2,π),
This paper starts with the discussion of the nature of inverse trigonometric functions. Through analyzing some mistakes, we introduce five points of attention in the learning of inverse trigonometric functions. 1. Note that the main value interval represents an angle or an evaluation with an inverse trigonometric function. It should be noted that the main value interval of the inverse trigonometric function. Example 1 If sinx=(3~(1/2))/5, x∈(π/2,π), try out the arcsine function. The wrong solution x=arcsin(3~(1/2))/5 [error analysis] arcsin(3~(1/2))/5∈(v,π/2), and x∈“π/2, π). Therefore, the above answer is incorrect. Positive solution ∵x∈(π/2,π),