Test 14
1.
\(\alpha+\beta=\samefrac{3\pi}{2},\ \sin\alpha=\samefrac14\)
\(\Rightarrow\cos(2\alpha+\beta)=?\)
A) \(\samefrac14\)B) \(\samefrac{\sqrt{15}}4\)C) \(-\samefrac14\)D) \(-\samefrac12\)E) \(-\samefrac1{\sqrt{15}}\)
2.
\(x+y=\samefrac\pi4,\ \cot x=\samefrac43\)
\(\Rightarrow\sin(3x+2y)=?\)
A) \(-\samefrac45\)B) \(-\samefrac35\)C) \(\samefrac12\)D) \(\samefrac35\)E) \(\samefrac45\)
3.
\(A+B=50^\circ,\ \sin(2A-10^\circ)=\samefrac35\)
\(\Rightarrow\cos2B=?\)
A) \(1\)B) \(\samefrac34\)C) \(\samefrac23\)D) \(\samefrac35\)E) \(\samefrac15\)
4.
\(A+B=30^\circ,\ \sin(3A+2B)=\samefrac45\)
\(\Rightarrow\tan B=?\)
A) \(\samefrac45\)B) \(\samefrac35\)C) \(\samefrac43\)D) \(\samefrac25\)E) \(\samefrac34\)
5.
\(3x=\sin(\pi+\theta),\ 4y=\cos(\pi-\theta)\)
\(\Rightarrow\text{ relation between }x\text{ and }y=?\)
A) \(3x-4y=0\)B) \(3x-4y-1=0\)C) \(3x+4y=0\)D) \(9x^2+16y^2=0\)E) \(9x^2+16y^2=1\)
6.
\(\text{The source figure consists of congruent squares; }\alpha\text{ is the marked angle.}\)
\(\tan\alpha+\cot\alpha=?\)
A) \(\samefrac23\)B) \(\samefrac32\)C) \(\samefrac49\)D) \(-\samefrac{13}{6}\)E) \(-\samefrac6{13}\)
7.
\(\text{The source figure consists of congruent squares; }\alpha\text{ is the marked angle.}\)
\(\tan\alpha=?\)
A) \(-\samefrac13\)B) \(-\samefrac12\)C) \(-\samefrac23\)D) \(-2\)E) \(-4\)
8.
\(ABCD\text{ right trapezoid},\ |AB|=8,\ |AD|=8,\ |DC|=14,\ m(\angle ABC)=\alpha\)
\(\Rightarrow\cos\alpha=?\)
A) \(\samefrac35\)B) \(-\samefrac45\)C) \(-\samefrac23\)D) \(-\samefrac35\)E) \(-\samefrac18\)