Question

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

`cos theta = 12/2`

Answer 1

`cos theta = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 12/15`

Let x be the opposite side.

By applying Pythagoras theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

225 = 𝑥² + 144

225 − 144 = 𝑥²

𝑥² = 81

𝑥 = 9

`sin theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 9/15`

`tan theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 9/12`

`cosec theta = 1/sin theta = (1/9)/15 = 15/9`

`sec theta = 1/cos theta = (1/12)/15 = 15/12`

`cot theta = 1/tan theta = (1/9)/12 = 12/9`