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Lesson List
第四章:部分分式 Partial Fraction
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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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Lesson: 7.1 任意角的三角函数 Trigonomeric Function Value of Any Angle [练习题]
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:
Package inputenc Error: 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:
Package inputenc Error: Unicode character ⁡ (U+2061)
leading text: $tan⁡

, 且A 在第三象限, 计算 cos Acosec 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:
Package inputenc Error: 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:
Package inputenc Error: 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.
sin x = -\frac{2}{3}, cos x > 0, 试计算tan xsec 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.
cos x = \frac{3}{8}, 求cosec x的值.
答案 Answer
\frac{8}{\sqrt{55}}x在第一象限

-\frac{8}{\sqrt{55}}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:
Package inputenc Error: 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:
Package inputenc Error: 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}
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Lesson List
第四章:部分分式 Partial Fraction
0/1
第六章:角的形成及单位 Angles and Measurements
0/1
第十三章: 方程组 Simultaneous Equations
0/1
第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
0/2
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