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Question
Find the values of other five trigonometric functions if ` tan x = - 5/12`, x lies in second quadrant.
Solution
tan x = −`5/12`
In ∆OAB, tan x = `"AB"/"OA"`
Here AB = 5 units
∴ OA = 12 units
∴ OB = = 13
OA = -12 (∵ in OX' direction)
AB = 5 (∵ in OY' direction)
OB = 13
sin x = `"AB"/"OB" = 5/13`'
cos x = `"OA"/"OB" = (-12)/13 = - 12/13`
cot x = `"OA"/"AB" = (-12)/5 = - 12/5`
sin x = `((-5)/12) xx ((-12)/13) = 5/13`
sin x = `5/13` gives cosec x = `13/5`
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