Answer:\(\frac{10}{9}\)
Step-by-step explanation:
Trigonometric is made up of two words trigon and metric .
Trigon means triangle and metric means measurement .
Trigonometric ratios basically define the relationship between the angles and sides .
We talk about trigonometric ratios in a right angled triangle .
For any triangle , there are six trigonometric ratios .
We have trigonometric ratios : \(\sin \theta \,,\,\cos \theta \,,\,\tan \theta \,,\,\csc \theta \,,\,\sec \theta \,,\,\cot \theta\) such that following relations hold :
\(\csc \theta =\frac{1}{\sin \theta }\\\\\sec \theta =\frac{1}{\cos \theta }\\\\\cot \theta =\frac{1}{\tan \theta }\)
Given: \(\cos \theta =\frac{9}{10}\)
To find : \(\sec \theta\)
Solution:
We know that \(\sec \theta =\frac{1}{\cos \theta }\) , so , \(\sec \theta =\frac{1}{\frac{9}{10} }=\frac{10}{9}\)
