Question

If the sine of an angle is 2/3, then cosine of that angle is

• A. Equal to 2/3
• B. Greater than 2/3
• C. Less than 2/3
• D. Infinite
• E. None of the above

Answer 1

Answer: (B)

Greater than 2/3

Let $p$= perpendicular.

$b$ = base.

$h$= hypotenuse.

$\sin \theta =\frac{2}{3}$.

Let $p=2k,h=3kb=\sqrt{{\left(3k\right)}^2-{\left(2k\right)}^2}=\sqrt{5(k{)}^2}=\sqrt{5}.k\therefore \cos \theta =\frac{b}{h}=\frac{\sqrt{5}k}{3k}>\frac{2}{3}$