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Question
Find the values of other five trigonometric functions if `cos x = -1/2`, x lies in third quadrant.
Solution
In ∆OAB,
cos x = - `1/2` = `"OA"/"OB"`
∴ AB = `sqrt("OB"^2 - "OA"^2)`
= `sqrt(4-1)` = ±`sqrt3`
AB is in the direction of axis OY'.
∴ AB = - `sqrt3`
⇒ OA = -1, AB = - `sqrt3`, OB = 2
sin x = `"AB"/"OB" = (-sqrt3)/-1`,
tan x = `"AB"/"OA" = (-sqrt3)/-1 = sqrt3`
cosec x = `"0B"/"AB" = (-2)/(-sqrt3)`
sec x = `"OB"/"OA" = 2/-1` = - 2
and cot x = `"OA"/"AB" = (-1)/(sqrt-3) = 1/sqrt3`.
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