The temperature of a body is measured both in \({ }^{\circ} \mathrm{C}\) and \({ }^{\circ} \mathrm{F}\). A…
The temperature of a body is measured both in \({ }^{\circ} \mathrm{C}\) and \({ }^{\circ} \mathrm{F}\). A graph is plotted with \({ }^{\circ} \mathrm{F}\) on \(X\)-axis and \({ }^{\circ} \mathrm{C}\) on \(Y\)-axis. Then, the cosine of angle between the graph and the \(X\)-axis is
0
\(\frac{9}{5}\)
\(\frac{5}{\sqrt{106}}\)
\(\frac{9}{\sqrt{106}}\)
Solution
The relation between celsius scale temperature and fahrenheit scale temperature is given as
\(\begin{aligned}
& & \frac{C}{5} & =\frac{F-32}{9} \\
\Rightarrow & & 9 C & =5 F-160 \\
\Rightarrow & & C & =\frac{5}{9} F-\frac{160}{9} \quad \ldots (i)
\end{aligned}\)
The graph between \(C\) and \(F\) is shown in the figure
Comparing Eq. (i) with line \(y=m x+C\), we get Slope of graph, \(m=\tan \theta=\frac{5}{9}\)
\(\therefore \quad \cos \theta=\frac{9}{\sqrt{106}}\)
