About Lesson
10.5 Graphical Solutions of Trigonometric Equations 三角方程式的图解法
(1) Sketch on the same diagram, the curves
and
for the interval
. State the number of solutions in the interval
of the equation
.
![Rendered by QuickLaTeX.com y = sin 2x](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-a1336d2387485129a833ff34d4510f46_l3.png)
![Rendered by QuickLaTeX.com y = |cosx|](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-69d5c2980545bfa6e4bf24f0b85e1716_l3.png)
![Rendered by QuickLaTeX.com -\pi \leq x \leq \pi](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-fbd372da239f45096738d4b8af7ad234_l3.png)
![Rendered by QuickLaTeX.com -\pi \leq x \leq \pi](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-fbd372da239f45096738d4b8af7ad234_l3.png)
![Rendered by QuickLaTeX.com |cosx| = sin2x](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-40e2e633e0e4f1b55c6856b1bcdc5445_l3.png)
在同一个图,描曲线 和
当
. 试说明在
的区间方程式
有多少个解.
Answer :
4
(2) Sketch
and
for
and find the number of solution for
.
![Rendered by QuickLaTeX.com y = 2cos 3x](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f7791fb1cd63201e33ba124e5f8f7ce6_l3.png)
![Rendered by QuickLaTeX.com y = -sin x](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-51aa47569d4b5e9c00aacfc2b8decea7_l3.png)
![Rendered by QuickLaTeX.com -180^{\circ} \leq x \leq 180^{\circ}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-fd91ed1cc622d8f675d47e2ca416bb77_l3.png)
![Rendered by QuickLaTeX.com 2cos 3x + sin x = 0](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-75657659ed6754471d759d7c449a5420_l3.png)
在中描
和
且求
有多少个实数解。
Answer :
6
(3) Find the number of solution for the equation
where
.
![Rendered by QuickLaTeX.com cos2x = 2sin3x](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-cea68ceefbcd05e75fbc06815472bee9_l3.png)
![Rendered by QuickLaTeX.com 0 \leq x \leq \pi](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7eec64d2b5026eccfa773b48598ec802_l3.png)
求在 中,
有多少个实数解。
Answer :
4
(4) Sketch the graph of
=
for
. By sketching a suitable straight line on the same diagram, find the number of solution for
+
=
.
![Rendered by QuickLaTeX.com y](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-4903bf5fc124494a1805bb0db9a6ae97_l3.png)
![Rendered by QuickLaTeX.com 3cos{2}(x+\frac{\pi}{2})](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-cdb729e63224ea8de42309962e0961d0_l3.png)
![Rendered by QuickLaTeX.com 0 \leq x \leq 2\pi](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-88a6cbac685e8082c2bac6ffda963180_l3.png)
![Rendered by QuickLaTeX.com cos{2}(x+\frac{\pi}{2})](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1390d48d5ab2cd59b4f2e0f269d52252_l3.png)
![Rendered by QuickLaTeX.com \frac{x}{\pi}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-34671918c3b902c75fd7f5d43e843fa5_l3.png)
![Rendered by QuickLaTeX.com 1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7297ed5d8a0649a927d31ac326d7d575_l3.png)
描图 =
当
. 在同一个图描一适当的直线,求
+
=
有多少个实数解有多少个实数解。
Answer :
5
(5) Sketch the graphs of
such that
.
Hence, obtain the number of solutions of
![Rendered by QuickLaTeX.com y = |cos2(x- \frac{1}{4}\pi)|](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-5f8dc88aaec9178f838648392f33dc88_l3.png)
![Rendered by QuickLaTeX.com 0 \leq x \leq 2\pi](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-88a6cbac685e8082c2bac6ffda963180_l3.png)
Hence, obtain the number of solutions of
![Rendered by QuickLaTeX.com x-\pi=\pi|cos{2}(x-\frac{1}{4}\pi)|](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3f06a12085e4a04cf0d779f08ad4358e_l3.png)
描图当
.
据此,找 有多少个实数解
Answer :
4