The missing pieces strategy is another method to compare two fractions. To tell which number is larger, you need to see which one is missing less. For example, you have 3/4 versus 4/5. Each of these fractions needs 1 to complete the whole. You need to subtract the numerator with one to compare them. For 3/4 we have 1/4 and for 4/5 we have 1/5. You know that if you complete 4/5 you will get 4. You know that 5 is greater than four. Therefore, 4/5 is larger than 3/4.

5 0

3 years ago

Which angle has a sine of -1/2 and a cosine of -√3/2

Sergeeva-Olga [200]

$\sin x=-\dfrac{1}{2} < 0\\\\\cos x=-\dfrac{\sqrt3}{2} < 0\\\\therefore\ x\in(180^o;\ 270^o)$

$\text{We know:}\ \tan x=\dfrac{\sin x}{\cos x}\\\\\text{therefore:}\ \tan x=\dfrac{-\frac{1}{2}}{-\frac{\sqrt3}{2}}=\dfrac{1}{2}\cdot\dfrac{2}{\sqrt3}=\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=\dfrac{\sqrt3}{3}$

$\tan x=\dfrac{\sqrt3}{3}\Rightarrow x=30^o+180^o\cdot k;\ k\in\mathbb{Z}$

$x\in(180^o;\ 270^o)\ therefore\ \boxed{x=30^o+180^o=210^o}$

8 0

3 years ago