Course Content
第四章:部分分式 Partial Fraction
0/1
第六章:角的形成及单位 Angles and Measurements
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第十三章: 方程组 Simultaneous Equations
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第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
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高中一 | 高级数学
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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
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