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Question
Find the values of other five trigonometric function if `sec x = 13/5`, x lies in fourth quadrant.
Solution
sec x = `13/5 = "OB"/"OA"`
Here OB = 13 units
∴ OA = 5 units
∴ AB = `sqrt("OB"^2 - "OA"^2)`
= ∴ AB = `sqrt(169-25)`
= ± 12
Now OA = 5 (in OX' direction)
AB = 12 (in 'OY' direction)
OB = 13
sin x = `"AB"/"OB" = (-12)/13 = -12/13, cos x = "OA"/"OB" = 5/13`
tan x = `"AB"/"OA" = (-12)/5 = -12/5, cos x = "OA"/"OB" = 5/13`
coses x = `"OB"/"AB" = 13/(-12) = -13/12`.
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