Section: 带有计算器的三角比 | 8.8 带有计算器的三角比

Section outline

Trigonometric Ratios with a Calculator
::带有计算器的三角比

There is a fixed sine, cosine, and tangent value for every angle, from $\begin{aligned} 0^{\circ} \end{aligned}$ to $\begin{aligned} 90^{\circ} \end{aligned}$ . Your scientific (or graphing) calculator knows all the trigonometric values for any angle. Your calculator, should have [SIN], [COS], and [TAN] buttons. You can use your calculator and the trigonometric ratios is to find the missing sides of a right triangle by setting up a trig equation.
::每个角度都有固定的正弦、余弦和正切值,从0到90。您的科学(或图形化)计算器知道任何角的所有三角值。您的计算器应该有[SIN]、[COS]和[TAN]按钮。您可以使用计算器,三角比是通过设置三角方程找到右三角形的缺失边。

What if you were given a 20-70-90 triangle? How could you find the sine, cosine, and tangent of the $\begin{aligned} 20^{\circ} \end{aligned}$ and $\begin{aligned} 70^{\circ} \end{aligned}$ angles?
::如果给了你一个20-70-90三角形呢?你怎么能找到20-70-70三角形的正弦、连弦和正弦?

Examples
::实例

Example 1
::例1

Find the length of the missing sides and round your answers to the nearest tenth:
::寻找缺失的边的长度, 并绕过您的答案到最近的十分之一 :

Use tangent for $\begin{aligned} x \end{aligned}$ and cosine for $\begin{aligned} y \end{aligned}$ .
::x 使用正切值, y 使用余弦。

$\begin{aligned} \tan 28^{\circ} & = \frac{x}{11} & \cos 28^{\circ} = \frac{11}{y} \\ 11 \cdot \tan 28^{\circ} & = x & \frac{11}{\cos 28^{\circ}} = y \\ x & \approx 5.8 & y \approx 12.5 \end{aligned}$

::{\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}28\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}28 {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}28\b0}x1111 cos28 {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}

Example 2
::例2

Find the length of the missing sides and round your answers to the nearest tenth:
::寻找缺失的边的长度, 并绕过您的答案到最近的十分之一 :

Use tangent for $\begin{aligned} y \end{aligned}$ and cosine for $\begin{aligned} x \end{aligned}$ .
::y 使用正切值, x 使用余弦。

$\begin{aligned} \tan 40^{\circ} & = \frac{y}{16} & \cos 40^{\circ} = \frac{16}{x} \\ 16 \cdot \tan 40^{\circ} & = y & \frac{16}{\cos 40^{\circ}} = x \\ y & \approx 13.4 & x \approx 20.9 \end{aligned}$

::{\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}40\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}40 {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}

Example 3
::例3

Find the trigonometric values, using your calculator:
::查找三角值, 使用您的计算器 :

$\begin{aligned} \sin 78^{\circ} \end{aligned}$ , $\begin{aligned} \cos 60^{\circ} \end{aligned}$ , $\begin{aligned} \tan 15^{\circ} \end{aligned}$
::7,8,8,8,8,8,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,5,5,5,5,5,5,5,5,5,8,8,8,8,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

Round to 4 decimal places.
::至小数点后四舍五入位数。

Depending on your calculator, you enter the degree and then press the trig button or the other way around. Also, make sure the mode of your calculator is in DEGREES.
::取决于您的计算器,您可以输入度,然后按三角按钮或反方向键。此外,请确定您的计算器模式在 DEGREES 中。

$\begin{aligned} \sin 78^{\circ} = 0.97815 \end{aligned}$
::778 0.97815

$\begin{aligned} \cos 60^{\circ} = 0.5 \end{aligned}$
:cos600.5)

$\begin{aligned} \tan 15^{\circ} = 0.26795 \end{aligned}$
::~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Example 4
::例4

Find the value of each variable. Round your answer to the nearest tenth.
::查找每个变量的值。将您的答案四舍五入到最接近的十分之一。

We are given the hypotenuse. Use sine to find $\begin{aligned} b \end{aligned}$ , and cosine to find $\begin{aligned} a \end{aligned}$ . Use your calculator to evaluate the of the angles.
::我们被赋予了下限。使用正弦来找到 b, 和 cosine 来找到 a。使用您的计算器来评估角度。

$\begin{aligned} \sin 22^{\circ} & = \frac{b}{30} & \cos 22^{\circ} = \frac{a}{30} \\ 30 \cdot \sin 22^{\circ} & = b & 30 \cdot \cos 22^{\circ} = a \\ b & \approx 11.2 & a \approx 27.8 \end{aligned}$

::

Example 5
::例5

Find the value of each variable. Round your answer to the nearest tenth.
::查找每个变量的值。将您的答案四舍五入到最接近的十分之一。

We are given the adjacent leg to $\begin{aligned} 42^{\circ} \end{aligned}$ . To find $\begin{aligned} c \end{aligned}$ , use cosine and use tangent to find $\begin{aligned} d \end{aligned}$ .
::我们被授予42的相邻腿。要找到 c, 使用余弦和正弦来找到 d。

$\begin{aligned} \cos 42^{\circ} & = \frac{a d j a c e n t}{h y p o t e n u s e} = \frac{9}{c} & \tan 42^{\circ} = \frac{o p p o s i t e}{a d j a c e n t} = \frac{d}{9} \\ c \cdot \cos 42^{\circ} & = 9 & 9 \cdot \tan 42^{\circ} = d \\ c & = \frac{9}{\cos 42^{\circ}} \approx 12.1 & d \approx 27.0 \end{aligned}$

::424412121277

Any time you use trigonometric ratios, use only the information that you are given. This will result in the most accurate answers.
::使用三角比时, 只能使用给您的信息。这将产生最准确的答案。

Review
::回顾

Use your calculator to find the value of each trig function below. Round to four decimal places. Note if you have a mode setting, make sure it is set to "Degree".
::使用您的计算器来查找以下每个 trig 函数的值。舍入到小数点后 4 位。注意, 如果您有一个模式设置, 请确定它被设置为“ degree ” 。

$\begin{aligned} \sin 24^{\circ} \end{aligned}$
::确实如此 24\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

$\begin{aligned} \cos 45^{\circ} \end{aligned}$
::{\pos(192,245)}翻譯: 翻譯: 翻譯: 翻譯: 翻譯:

$\begin{aligned} \tan 88^{\circ} \end{aligned}$
::{\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}现在... {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}现在... {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}现在...

$\begin{aligned} \sin 43^{\circ} \end{aligned}$
::问题43 - . · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·

$\begin{aligned} \tan 12^{\circ} \end{aligned}$
::{\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}为什么?

$\begin{aligned} \cos 79^{\circ} \end{aligned}$
:cos79) (cos 79) (cos 79) (cos 79)

$\begin{aligned} \sin 82^{\circ} \end{aligned}$
::- 确实有问题吗? - . . . . . . . . .

Find the length of the missing sides. Round your answers to the nearest tenth.
::查找缺失方的长度。将您的答案转至最近的十分之一。

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

Section outline

Trigonometric Ratios with a Calculator ::带有计算器的三角比

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Trigonometric Ratios with a Calculator
::带有计算器的三角比

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源