Test 7
1.
\(0
\(\sin x-\cos x=?\)
A) \(-\samefrac15\)B) \(\samefrac15\)C) \(\samefrac25\)D) \(1\)E) \(\samefrac75\)
2.
\(x\in(0,\samefrac\pi2),\ \sin x=\samefrac{12}{13}\)
\(\tan x+\cot x=?\)
A) \(\samefrac5{12}\)B) \(\samefrac{12}{13}\)C) \(\samefrac{60}{13}\)D) \(\samefrac{12}{5}\)E) \(\samefrac{169}{60}\)
3.
\(0
\(\samefrac{\tan x}{\cot x}=?\)
A) \(\samefrac{\sqrt3}{2}\)B) \(\samefrac13\)C) \(3\)D) \(\samefrac{10}{3}\)E) \(2\sqrt5\)
4.
\(0
\(\cos x=?\)
A) \(\samefrac1{10}\)B) \(-\samefrac15\)C) \(\samefrac1{\sqrt5}\)D) \(\samefrac2{\sqrt5}\)E) \(\samefrac3{\sqrt5}\)
5.
\(0
\(\tan x+\cot x=?\)
A) \(\samefrac1{a\sqrt{1-a}}\)B) \(\samefrac1{\sqrt{1-a^2}}\)C) \(\samefrac1{a\sqrt{1-a^2}}\)D) \(\samefrac a{\sqrt{1-a^2}}\)E) \(\samefrac1{\sqrt{a-a^2}}\)
6.
\(x\in(0,\samefrac\pi2),\ 4\sin x=3\cos x\)
\(2\sin x\cos x=?\)
A) \(\samefrac35\)B) \(\samefrac34\)C) \(\samefrac{12}{25}\)D) \(\samefrac{24}{25}\)E) \(\samefrac{12}{5}\)
7.
\(0
\(\samefrac{\cos x+\sin x}{\cos x-\sin x}=2\)
\(\sec x=?\)
A) \(\sqrt{10}\)B) \(\samefrac{\sqrt{10}}3\)C) \(\samefrac13\)D) \(\samefrac3{\sqrt{10}}\)E) \(3\)
8.
\(\text{The source figure consists of congruent squares; }\alpha\text{ is the marked diagonal angle.}\)
\(\cot\alpha=?\)
A) \(\samefrac23\)B) \(\samefrac32\)C) \(2\)D) \(\samefrac52\)E) \(3\)