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प्रश्न
Find the other trigonometric functions:
If cot x = `3/4`, x lies in the third quadrant.
उत्तर
We have cot x =`3/4`
∴ cosec2x = 1 + cot2x
= `1 + (3/4)^2`
= `1 + 9/16`
= `25/16`
∴ cosec x = `± 5/4`
But x lies in the third quadrant
∴ cosec x is negative
∴ cosec x= `-5/4`
∴ sin x = `1/("cosec"x) = 1/((-5/4)) = -4/5`
Now, cot x = `cosx/sinx = 3/4`
∴ cos x = `3/4 sinx = 3/4(-4/5) = -3/5`
sec x = `1/cosx = 1/((-3/5)) = -5/3`
tan x = `1/cotx =1/(3/4) = 4/3`
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