Question

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`sec theta = 13/5`

Answer 1

`sec theta = "ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 13/5`

Now consider a right-angled Δ^le ABC

By applying Pythagoras theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

169 = 𝑥² + 25

𝑥² = 169 − 25 = 144

𝑥 = 12

`cos theta = 1/sec theta = (1/13)/5 = 5/13`

`tan theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 12/5`

`sin theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 12/13`

`cosect theta = 1/sin theta = 1/(12/13) = 13/12`

`sec theta = 1/cos theta = 1/(5/13) = 13/5`

`cot theta = 1/tan theta = 1/(12/5) = 5/12`