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Question
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
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Solution
In the diagram ON = `5/7`
PN = `(2sqrt(6))/7`
ON2 + NP2 = OP2
(i.e) `25/49 + 24/49 = 49/49` = OP2
⇒ OP = 1
sin θ = `"PN"/"OP"`
= `(2sqrt(6)/7)/1`
= `(2sqrt(6))/7`
cos θ = `"ON"/"OP"`
= `(5/7)/1`
= `5/7`
tan θ = `"PN"/"ON"`
= `((2sqrt(6))/7)/(5/7)`
= `(2sqrt(6))/5`
cosec θ = `1/sintheta = 7/(2sqrt(6))`
sec θ = `1/costheta = 7/5`
cot θ = `1/tantheta = 5/(2sqrt(6))`
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