Question

The temperature of a body is measured both in ${}^{\circ }C$ and ${}^{\circ }F$. A graph is plotted with ${}^{\circ }F$ on $x$-axis and ${}^{\circ }C$ on $y$-axis. Then the cosine of angle between the graph and the $x$ axis is_________

• A. $0$
• B. $\frac{9}{5}$
• C. $\frac{5}{\sqrt{106}}$
• D. $\frac{9}{\sqrt{106}}$

Answer 1

Answer: (D)

The relation between celsius scale temperature and fahrenheit scale temperature is given as
$\frac{C}{5}=\frac{F-32}{9}$
$\Rightarrow 9C=5F-160$
$\Rightarrow C=\frac{5}{9}F-\frac{160}{9}...(i)$
The graph between $C$ and $F$ is shown in the figure

Comparing Eq. (i) with line $y=mx+C$, we get
Slope of graph, $m=\tan \theta =\frac{5}{9}$
$\therefore \cos \theta =\frac{9}{\sqrt{106}}$