If cot x = 12/5 , x lies in 3rd quadrant, find other five t-ratio.
Answers
Answer:
Step-by-step explanation
★ Given :-
- cotx = 12/5
- x belongs to 3rd Quadrant
★ To find :-
- Other 5 Trigonometric ratios
★ To know :-
- In 3rd Quadrant
- ➙ sinA is negative
- ➙ cosA is negtive
- ➙ tanA is positive
- ➙ cosecA is negative
- ➙ secA is negative
- ➙ cotA is positive
★ Trigonometric ratios :-
➙sinA = opposite side / Hypotenuse
➙cosA = adjacent side / Hypotenuse
➙ tanA = opposite side/ Adjacent side
➙ cosecA = Hypotenuse/ opposite side
➙ secA = Hypotenuse/ adjacent side
➙ cotA = Adjacent side/opposite side
★ S O L U T I O N :-
As they given that ,
cotx = 12/5 i.e
- Adjacent side = 12
- Opposite side= 5
By Pythagoras theorem ,
(Opposite side)² + (Adjacent side)² = (Hypotenuse)²
(5)² + (12)² = (Hypotenuse)²
25 + 144 = (hyp)²
169 = (hyp)²
(13)² = (hyp)²
Hypotenuse = 13
Now, finding the Trigonometric ratios,
sinx = opposite/hypotenuse
sinx = 5/13
As it is in 3rd Quadrant i.e sin is negative So, it will be
★sinx = -5/13
cosx = adjacent/hypotenuse
cosx = 12/13
As it is in 3rd Quadrant i.e cos is negative So, it will be
★cosx = -12/13
tanx = opposite/adjacent
tanx = 5/12
As it is in 3rd Quadrant i.e tan is positive . So, it will be,
★tanx = 5/12
cosecx = Hypotenuse/opposite
cosec x = 13/5
As it is in 3rd Quadrant i.e cosec is negative So, it will be
★cosecx = -13/5
secx = Hypotenuse/adjacent
secx = 13/12
As it is in 3rd Quadrant i.e sec is negative So, it will be
★secx = -13/12
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★F I N A L - A N S W E R S :-
➜sinx = -5/13
➜cosx = -12/13
➜tanx = 5/12
➜cosecx = -13/5
➜secx = -13/12