Question

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

`tan theta = 8/15`

Answer 1

We know that `tan theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 8/15`

Now consider a right-angled Δ^le ABC.

By applying Pythagoras theorem

𝐴𝐶² = 𝐴𝐵² + 𝐵𝐶²

𝑥² = 8² + 15²

𝑥² = 225 + 64 = 289

`x  = sqrt289 = 17`

`sin theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 8/17`

`cos theta = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒" = 15/17`

`tan theta = "𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒"/"𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒" = 8/15`

`cot theta = 1/tan theta = 1/(8/15) = 15/8`

`cosec theta = 1/sin theta = (1/8)/17 = 17/8`

`sec theta = 1/cos theta= (1/15)/17 = 17/15`