Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

`cot theta = 12/5`

Answer 1

`cot alpha = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒" = 12/5`

Now consider a right-angled Δ^le ABC,

By applying Pythagoras theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

𝑥² = 25 + 144

`x^2 = 169 = sqrt169`

𝑥 = 13

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

`sin theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 5/13`

`cos theta = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 12/13`

`cosec theta = 1/sin theta = 1/(5/13) = 13/5`

`sec theta = 1/cos theta = 1/(12/13) = 13/12`