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Question
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
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Solution
`cos theta = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 12/15`
Let x be the opposite side.
By applying Pythagoras theorem
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
225 = ๐ฅ2 + 144
225 − 144 = ๐ฅ2
๐ฅ2 = 81
๐ฅ = 9
`sin theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 9/15`
`tan theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 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`
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