7.1 任意角的三角函数 Trigonomeric Function Value of Any Angle [练习题] - 独中课程 | 线上补习

高中一 | 高级数学

About Lesson

(1)
Convert the following trigonometric functions to acute trigonometric functions.
化下列各三角函数为锐角三角函数
(a) $cos 125^{\circ}$
(b) $cosec 200^{\circ}$
(c) $tan 550^{\circ}$
(d) $sin (-226^{\circ}$ )
(e) $cot \frac{11\pi}{6}$
(f) $sec \frac{14\pi}{3}$

答案 Answer

(a) $-cos 55^{\circ}$
(b) $-cosec 20^{\circ}$
(c) $tan 10^{\circ}$
(d) $sin 46^{\circ}$
(e) $-cot \frac{\pi}{6}$
(f) $-sec \frac{\pi}{3}$

(2)
Given that

*** QuickLaTeX cannot compile formula:
tan⁡A= \frac{8}{15}

*** Error message:
Unicode character ⁡ (U+2061)
leading text: $tan⁡

, where $A$ is in the third quadrant, calculate $cos A$ and $cosec A$
已知

*** QuickLaTeX cannot compile formula:
tan⁡A= \frac{8}{15}

*** Error message:
Unicode character ⁡ (U+2061)
leading text: $tan⁡

, 且A 在第三象限, 计算 $cos A$ 和 $cosec A$ 。

答案 Answer

$-\frac{15}{17}$ ， $-\frac{17}{8}$

(3)
Given that $270^{\circ}$ < $A$ < $360^{\circ}$ , and $cos A = \frac{5}{13}$ , find the value of

*** QuickLaTeX cannot compile formula:
\frac{13 sin⁡A+5 sec⁡A}{3 tan⁡A+cose A}

*** Error message:
Unicode character ⁡ (U+2061)
leading text: $\frac{13 sin⁡A+5 sec⁡A}{3 tan⁡A+cose A}

已知 $270^{\circ}$ < $A$ < $360^{\circ}$ 以及 $cos A = \frac{5}{13}$ , 求

*** QuickLaTeX cannot compile formula:
\frac{13 sin⁡A+5 sec⁡A}{3 tan⁡A+cose A}

*** Error message:
Unicode character ⁡ (U+2061)
leading text: $\frac{13 sin⁡A+5 sec⁡A}{3 tan⁡A+cose A}

的值

答案 Answer

$-\frac{60}{497}$

(4)
If $sin x = -\frac{2}{3}, cos x > 0$ , calculate the values of $tan x$ and $sec x$ .
若 $sin x = -\frac{2}{3}, cos x > 0$ , 试计算 $tan x$ 和 $sec x$ 的值。

答案 Answer

$-\frac{2}{\sqrt5}$ ， $-\frac{3}{\sqrt{5}}$

(5)
If $cos x = \frac{3}{8}$ , calculate the values of $cosec x$ .
若 $cos x = \frac{3}{8}$ , 求 $cosec x$ 的值.

答案 Answer

$\frac{8}{\sqrt{55}}$ 当 $x$ 在第一象限

$-\frac{8}{\sqrt{55}}$ 当 $x$ 在第四象限

(6)
If 12tan x = 5, sin x < 0, calculate the value of

*** QuickLaTeX cannot compile formula:
\frac{2sin⁡x+sec⁡x}{4 cot⁡x-3 cos⁡x}

*** Error message:
Unicode character ⁡ (U+2061)
leading text: $\frac{2sin⁡x+sec⁡x}{4 cot⁡x-3 cos⁡x}

若 12tan x = 5, sin x < 0, 求

*** QuickLaTeX cannot compile formula:
\frac{2sin⁡x+sec⁡x}{4 cot⁡x-3 cos⁡x}

*** Error message:
Unicode character ⁡ (U+2061)
leading text: $\frac{2sin⁡x+sec⁡x}{4 cot⁡x-3 cos⁡x}

的值。

答案 Answer

$-\frac{1445}{9648}$