Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS1 Mark
Question
If cot x $= -\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.
✓
Answer
Given: cot x = $= -\frac{5}{12}$, x lies in second quadrant
Since cot x = $\begin{equation} -\frac{5}{12} \end{equation}$, we have
tan x = $\begin{equation} -\frac{12}{5} \end{equation}$
Now $sec^2 x = 1 + tan^2 x = 1 + \begin{equation} \frac{144}{25}=\frac{169}{25} \end{equation}$
Hence sec x = $\begin{equation} =\pm\frac{13}{5} \end{equation}$
Since x lies in second quadrant, sec x will be negative. Therefore
sec x = $\begin{equation} -\frac{13}{5} \end{equation}$,
Which also gives
cos x = $\begin{equation} -\frac{5}{13} \end{equation}$
Further, we have
sin x = tan x cos x = $\begin{equation} \left(-\frac{12}{5}\right) \times\left(-\frac{5}{13}\right)=\frac{12}{13} \end{equation}$
and cosec x = $\begin{equation} \frac{1}{\sin x}=\frac{13}{12} \end{equation}$
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