# Given sec θ = 13/12 , calculate all other trigonometric ratios. - Mathematics

Given sec θ = 13/12 , calculate all other trigonometric ratios.

#### Solution

Consider a right-angle triangle ΔABC, right-angled at point B.

sec theta = "Hypotenuse"/"Side adjacent to "angle theta

13/12 = (AC)/(AB)

If AC is 13k, AB will be 12k, where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain

(AC)2 = (AB)2 + (BC)2

(13k)2 = (12k)2 + (BC)2

169k2 = 144k2 + BC2

25k2 = BC2

BC = 5k

sin theta = (

cos theta = (

tan theta = (

cot theta = (

cosec theta = (

Concept: Trigonometric Ratios
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 8 Introduction to Trigonometry
Exercise 8.1 | Q 5 | Page 181