Test 36
1.
\(0\le x<360^\circ,\ \tan x=\samefrac{\sqrt3}{3}\)
\(\Rightarrow S.S.=?\)
A) \(\{60^\circ,120^\circ\}\)B) \(\{60^\circ,240^\circ\}\)C) \(\{30^\circ,210^\circ\}\)D) \(\{60^\circ,300^\circ\}\)E) \(\{240^\circ,300^\circ\}\)
2.
\(0\le x<90^\circ,\ \samefrac{\cos x+\cos3x+\cos5x}{\sin x+\sin3x+\sin5x}=\samefrac{\sqrt3}{3}\)
\(\Rightarrow S.S.=?\)
A) \(\{20^\circ\}\)B) \(\{30^\circ\}\)C) \(\{40^\circ\}\)D) \(\{20^\circ,60^\circ\}\)E) \(\{20^\circ,80^\circ\}\)
3.
\(0\le x<180^\circ,\ \tan(7x+20^\circ)=\tan(5x+60^\circ)\)
\(\Rightarrow S.S.=?\)
A) \(\{20^\circ,110^\circ\}\)B) \(\{70^\circ,120^\circ\}\)C) \(\{70^\circ,160^\circ\}\)D) \(\{80^\circ,130^\circ\}\)E) \(\{50^\circ,140^\circ\}\)
4.
\(\cot x=-1\)
\(\Rightarrow S.S.=?\)
A) \(\{\samefrac{3\pi}{4}+k\pi\}\)B) \(\{\samefrac\pi4+k\pi\}\)C) \(\{\samefrac{5\pi}{4}+k\pi\}\)D) \(\{\samefrac\pi3+k\pi\}\)E) \(\{\samefrac\pi6+k\pi\}\)
5.
\(0\le x<\pi,\ \cot6x=\cot(4x+\samefrac\pi3)\)
\(\Rightarrow S.S.=?\)
A) \(\{\samefrac\pi3,\samefrac{2\pi}{3}\}\)B) \(\{\samefrac\pi6,\samefrac{3\pi}{2}\}\)C) \(\{\samefrac\pi6,\samefrac{2\pi}{3}\}\)D) \(\{\samefrac\pi6,\samefrac{7\pi}{6}\}\)E) \(\{\samefrac\pi4,\samefrac{2\pi}{3}\}\)
6.
\(0\le x<2\pi,\ A=3\cos x-5\sin x\)
\(\Rightarrow\max(A)=?\)
A) \(4\)B) \(\sqrt{17}\)C) \(5\)D) \(\sqrt{34}\)E) \(6\)
7.
\(0\le x<180^\circ,\ \cos x-\sqrt3\sin x=0\)
\(\Rightarrow S.S.=?\)
A) \(\{30^\circ\}\)B) \(\{60^\circ\}\)C) \(\{90^\circ\}\)D) \(\{120^\circ\}\)E) \(\{150^\circ\}\)
8.
\(\sin x+\sqrt3\cos x=0\)
\(\Rightarrow S.S.=?\)
A) \(\{\samefrac{2\pi}{3}+k\pi\}\)B) \(\{\samefrac{2\pi}{5}+k\pi\}\)C) \(\{\samefrac\pi6+k\pi\}\)D) \(\{\samefrac{3\pi}{4}+k\pi\}\)E) \(\{\samefrac\pi3+k\pi\}\)