Test 37
1.
ABCD is a square. D, E, C and F are collinear in that order.
\(|DE|=|EC|=|CF|\)
\(m(FAE)=x\)
\(\Rightarrow\tan x=?\)
A) \(\samefrac18\)B) \(\samefrac17\)C) \(\samefrac16\)D) \(\samefrac15\)E) \(\samefrac47\)
2.
\(0\le x\le2\pi\)
\(3\cos^2x-7\cos x+4=0\)
\(\Rightarrow x=?\)
A) \(0\)B) \(\samefrac\pi6\)C) \(\samefrac\pi2\)D) \(\pi\)E) \(\samefrac{3\pi}{2}\)
3.
\(N(0,6),\ M(8,0)\)
P lies on segment NM.
\(m(PON)=\theta\)
\(|MP|=|MO|\)
\(\Rightarrow\tan\theta=?\)
A) \(\sqrt3\)B) \(\samefrac13\)C) \(3\)D) \(\samefrac14\)E) \(\samefrac1{\sqrt2}\)
4.
AB is perpendicular to AC and D lies on AC.
\(m(BDA)=60^\circ\)
\(m(DBC)=15^\circ\)
\(|CD|=4\)
\(\Rightarrow|AB|=?\)
A) \(\sqrt3\)B) \(2\sqrt3\)C) \(4\)D) \(6+2\sqrt3\)E) \(12\)
5.
ABCD is a rhombus. E lies on AB and F lies on DC.
\(|AD|=6\)
\(m(A)=120^\circ\)
\(|BE|=|DF|=2\)
\(\Rightarrow|EF|=?\)
A) \(2\sqrt7\)B) \(\samefrac{4\sqrt7}{3}\)C) \(3\sqrt2\)D) \(2\sqrt{10}\)E) \(2\sqrt{13}\)
6.
\(8a=\samefrac\pi2\)
\(\samefrac{\cos(3a)+\cos(5a)}{\cos a\cdot\sin(8a)}=?\)
A) \(-1\)B) \(\samefrac12\)C) \(\samefrac{\sqrt3}{2}\)D) \(\sqrt2\)E) \(\samefrac{\sqrt2}{2}\)
7.
In triangle ABC, D lies on BC.
\(|AD|=|BD|=|DC|\)
\(\cot C=2\)
\(\Rightarrow\tan B=?\)
A) \(\samefrac12\)B) \(\samefrac{\sqrt3}{2}\)C) \(\samefrac32\)D) \(2\)E) \(3\)
8.
\(\mathrm{I.}\ \sin105^\circ\)
\(\mathrm{II.}\ \tan170^\circ\)
\(\mathrm{III.}\ \cos250^\circ\)
\(\mathrm{IV.}\ \cot265^\circ\)
What are the signs of these expressions respectively?
A) \(+,-,+,-\)B) \(-,-,-,+\)C) \(+,-,-,+\)D) \(-,-,-,-\)E) \(+,-,-,-\)