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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

10.5 三角方程式的图解法 Graphical Solutions of Trigonometric Equations

10.5 Graphical Solutions of Trigonometric Equations 三角方程式的图解法


 

(1) Sketch on the same diagram, the curves y = sin 2x and y = |cosx| for the interval -\pi \leq x \leq \pi. State the number of solutions in the interval -\pi \leq x \leq \pi of the equation |cosx| = sin2x.

在同一个图,描曲线 y = sin 2xy = |cosx|-\pi \leq x \leq \pi. 试说明在 -\pi \leq x \leq \pi 的区间方程式 |cosx| = sin2x 有多少个解.

Answer :
4
(2) Sketch y = 2cos 3x and y = -sin x for -180^{\circ} \leq x \leq 180^{\circ} and find the number of solution for 2cos 3x + sin x = 0.

-180^{\circ} \leq x \leq 180^{\circ}中描y = 2cos 3xy = -sin x 且求 2cos 3x + sin x = 0 有多少个实数解。

Answer :
6
(3) Find the number of solution for the equation cos2x = 2sin3x where 0 \leq x \leq \pi.

求在0 \leq x \leq \pi 中,cos2x = 2sin3x 有多少个实数解。

Answer :
4
(4)  Sketch the graph of y=3cos{2}(x+\frac{\pi}{2}) for 0 \leq x \leq 2\pi. By sketching a suitable straight line on the same diagram, find the number of solution for cos{2}(x+\frac{\pi}{2})+\frac{x}{\pi}=1.

描图 y=3cos{2}(x+\frac{\pi}{2})0 \leq x \leq 2\pi. 在同一个图描一适当的直线,求 cos{2}(x+\frac{\pi}{2})+\frac{x}{\pi}=1 有多少个实数解有多少个实数解。

Answer :
5
(5)  Sketch the graphs of y = |cos2(x-  \frac{1}{4}\pi)| such that 0 \leq x \leq 2\pi.
Hence, obtain the number of solutions of x-\pi=\pi|cos{2}(x-\frac{1}{4}\pi)|

描图y = |cos2(x-  \frac{1}{4}\pi)|0 \leq x \leq 2\pi.
据此,找 x-\pi=\pi|cos{2}(x-\frac{1}{4}\pi)| 有多少个实数解

Answer :
4