Test 38
1.
\(\sin20^\circ=A\)
Which of the following is equal to A?
A) \(\sin70^\circ\)B) \(\cos140^\circ\)C) \(\cos50^\circ\)D) \(-\cos110^\circ\)E) \(\cos(-50^\circ)\)
2.
\(0\le x\le\samefrac\pi2\)
\(\cot x=\samefrac12\)
\(\Rightarrow\cos^2x-\cos x\sin x=?\)
A) \(-1\)B) \(-\samefrac13\)C) \(-\samefrac15\)D) \(0\)E) \(\samefrac23\)
3.
AB is perpendicular to BC. D is the midpoint of AB.
\(m(BAC)=30^\circ\)
\(m(DCB)=\alpha\)
\(\Rightarrow\tan\alpha=?\)
A) \(\samefrac{\sqrt3}{2}\)B) \(\samefrac{\sqrt5}{2}\)C) \(\samefrac{\sqrt5}{3}\)D) \(\sqrt3\)E) \(2\sqrt3\)
4.
The figure consists of congruent squares.
\(\Rightarrow\cot\theta=?\)
A) \(\samefrac16\)B) \(\samefrac15\)C) \(\samefrac14\)D) \(\samefrac13\)E) \(\samefrac12\)
5.
\(0\le x<\samefrac\pi2\)
\(\cot x=\samefrac34\)
\(\Rightarrow\sin^2x-\cos^2x=?\)
A) \(\samefrac1{25}\)B) \(\samefrac2{25}\)C) \(\samefrac7{25}\)D) \(\samefrac45\)E) \(1\)
6.
\(0\le x<\samefrac\pi2\)
\(\samefrac1{\cos x}=\samefrac3{\sin x}\)
\(\Rightarrow\cos x=?\)
A) \(\samefrac13\)B) \(3\)C) \(\samefrac1{\sqrt{10}}\)D) \(\samefrac3{\sqrt{10}}\)E) \(\samefrac3{10}\)
7.
\(0\le x<\samefrac\pi2\)
\(\samefrac1{1-\sin x}-\samefrac1{1+\sin x}=\samefrac8{15}\)
\(\Rightarrow\sin x=?\)
A) \(\samefrac23\)B) \(\samefrac12\)C) \(\samefrac14\)D) \(\samefrac3{15}\)E) \(\samefrac1{15}\)
8.
\(\cos^2x-\sin^2x=\samefrac23\)
\(\Rightarrow\sin^2(2x)=?\)
A) \(\samefrac23\)B) \(\samefrac49\)C) \(\samefrac59\)D) \(-\samefrac12\)E) \(-\samefrac23\)