Question

Find cot, cos0, and sect, where o is the angle shown in the figure.Give exact values, not decimal approximations.

Answer 1

Given:

A triangle is given as below

Find:

we have to find the values of cotangent, cosine and secant at theta.

Explanation:

we know,

$\begin{gathered} cos\theta=\frac{Base}{Hypotenuse}=\frac{6}{11} \\ sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{6}{11}}=\frac{11}{6} \\ tan^2\theta=sec^2\theta-1=\frac{121}{36}-1=\frac{85}{36} \\ cot^2\theta=\frac{1}{tan^{^2}\theta}=\frac{1}{\frac{85}{36}}=\frac{36}{85} \\ cot\theta=\pm\sqrt{\frac{36}{85}} \end{gathered}$

since, angle is less than 90 degree, so we will take only positive value of cotangent,

Therefore, the required values are given as below

$\begin{gathered} cot\theta=\sqrt{\frac{36}{85}} \\ cos\theta=\frac{6}{11} \\ sec\theta=\frac{11}{6} \end{gathered}$