Question

If sinA=4/5 then find the value of CosA, tanA, secA, CosecA, cotA
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Answer 1

Step-by-step explanation:

Here, base = b, perpendicular = p, hypotenuse = h.

sinA = 4/5 = p/h

 Using Pythagoras theorem,   b = 3

Hence,

cosA = b/h = 3/5

tanA = h/b = 4/3

secA = h/b = 5/3

cosecA = h/p = 5/4

cotA = b/h = 3/4  

Answer 2

Let ,

Opposite side = O.S

Adjacent side = A.S

Hypotenuse = A

Given ,

$\sf sinA=\dfrac{4}{5}\\\\\to \sf \dfrac{O.P}{H}=\dfrac{4}{5}$

So ,

O.S = 4

H = 5

Apply Pythagoras theorem ,

⇒ (O.S)² + (A.S)² = (H)²

⇒ 4² + (A.S)² = 5²

⇒ 16 + (A.S)² = 25

⇒ (A.S)² = 25 - 16

⇒ A.S = √9

⇒ A.S = 3

$\to \sf CosA=\dfrac{A.S}{H}=\dfrac{3}{5}\\\\\to \sf SecA=\dfrac{H}{A.S}=\dfrac{5}{3}\\\\\to \sf CscA=\dfrac{H}{O.S}=\dfrac{5}{3}\\\\\to \sf TanA=\dfrac{O.S}{A.S}=\dfrac{4}{3}\\\\\to \sf CotA=\dfrac{A.S}{O.S}=\dfrac{3}{4}$