Chapter 9, Problem 1CR

To determine

Toevaluate other trigonometric ratios for given trigonometric ratio.

Answer to Problem 1CR

  $\sin \theta =\frac{\sqrt{85}}{11}$ , $\sec \theta \text{=}\frac{11}{6}$ , $\cot \theta =\frac{6}{\sqrt{85}}$ , $\tan \theta =\frac{\sqrt{85}}{6}$ , $\cos ec\theta =\frac{11}{\sqrt{85}}$

Explanation of Solution

Given Information:

  $\text{cos}\theta \text{=}\frac{6}{11}$

Calculation:

Given $\text{cos}\theta \text{=}\frac{6}{11}$

Therefore, $\sec \theta \text{=}\frac{11}{6}$

  $\begin{array}{l}\sin \theta =\sqrt{1-{\cos }^2}\theta \\ \sin \theta =\sqrt{1-{\left(\frac{6}{11}\right)}^2}\\ \sin \theta =\sqrt{1-\frac{36}{121}}\\ \sin \theta =\sqrt{\frac{121-36}{121}}\\ \sin \theta =\sqrt{\frac{85}{121}}\\ \sin \theta =\frac{\sqrt{85}}{11}\end{array}$

  $\cos ec\theta =\frac{11}{\sqrt{85}}$

And

  $\begin{array}{l}\tan \theta =\frac{\sin \theta }{\cos \theta }\\ \tan \theta =\frac{\frac{\sqrt{85}}{11}}{\frac{6}{11}}\\ \tan \theta =\frac{\sqrt{85}}{6}\end{array}$

  $\cot \theta =\frac{6}{\sqrt{85}}$