摘要:基本三角三角三角三角三角测量

When we apply trigonometry, it is important to have a complete toolbox of mathematical techniques to use. Trigonometric functions extend Euclidean geometry to solve problems in many areas, such as surveying and astrophysics.
::当我们应用三角测量时,必须有一个完整的数学技术工具箱来使用。三角测量功能扩展了欧几里德几何学,以解决许多领域的问题,例如测量和天体物理学。

Chapter Summary
::章次摘要

In this chapter we learned about:
::在本章中,我们了解到:

Special Right Triangles
::特别右三角

播放段落
• A 30-60-90 right triangle has side ratios  $\begin{array}{r}x,x\sqrt{3},\text{ and }2x\end{array}$ . 
  ::A 30-60-90右三角有侧翼比率x、x3和2。
播放段落
• A 45-45-90 right triangle has side ratios  $\begin{array}{r}x,x,\text{ and }x\sqrt{2}\end{array}$ . 
  ::A 45-45-90右三角形有侧比x、x和x2。
播放段落
• Pythagorean triples are special right triangles with integer sides.
  ::毕达哥林三重三角形是特殊的右三角形,有整边。

Right Triangle Trigonometry
::右三角三角三角三角三角形

播放段落
• $\begin{array}{r}\sin \theta =\frac{opp}{hyp}\end{array}$
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播放段落
• $\begin{array}{r}\cos \theta =\frac{adj}{hyp}\end{array}$
  ::
播放段落
• $\begin{array}{r}\tan \theta =\frac{opp}{adj}\end{array}$
  ::
播放段落
• $\begin{array}{r}\cot \theta =\frac{adj}{opp}\end{array}$
  ::cotadjopp 连接
播放段落
• $\begin{array}{r}\sec \theta =\frac{hyp}{adj}\end{array}$
  ::
播放段落
• $\begin{array}{r}\csc \theta =\frac{hyp}{opp}\end{array}$
  ::csc

Law of Cosines
::科士法

播放段落
• $\begin{array}{r}{a}^2=b^2+c^2-2bc\cos A\\ b^2=a^2+c^2-2ac\cos B\\ c^2=a^2+b^2-2ab\cos C\end{array}$
  ::a2=b2+c2+c2-2bccosAb2=a2+c2-2acosBc2=a2+b2-2abcosC

Law of Sines
::Sines法律

播放段落
• $\begin{array}{r}\text{Form}1:\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\\ \\ \text{Form}2:\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\end{array}$
  ::表格1:sinaa=sinBb=sinCform2:asinA=bsinB=csinC

Area Formulas
::区域公式

播放段落
• $\begin{array}{r}\text{Area}=\frac{1}{2}\cdot a\cdot b\sin C\end{array}$  
  ::面积=12absinC
播放段落
• Heron's Formula: $\begin{array}{r}\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}\end{array}$  with $\begin{array}{r}s=\frac{a+b+c}{2}\end{array}$   
  ::Heron的公式:面积=(s-a)(s-b)(s-c)和s=a+b+c2

Review
::回顾

Try the following cumulative review problems to practice the concepts in this chapter:
::尝试下列累积审查问题来实践本章中的概念: