Question

Find TanQ if SinQ=4/5

Answer 1

Solution:

These are trigonometric ratios of right angled triangle.

sin Q = Perpendicular/Hypotenuse = 4/5

cos Q = Base/Hypotenuse

tan Q = Perpendicular/Base

From above we can say that,

Perpendicular = 4

Hypotenuse = 5

Base = x       [Let it be x]

By Pythagoras Theorem,

(Perpendicular)² + (Base)² = (Hypotenuse)²

4² + x² = 5²

16 + x² = 25

x² = 25 - 16

x² = 9

x = √9

x = 3

Base = x = 3

tan Q = Perpendicular/Base = 4/3

The value of tan Q is 4/3

Answer 2

Given :  SinQ=4/5

To find :  Value of TanQ

Solution:

we know that

Sin²α + Cos²α  = 1

=>  Sin²Q + Cos²Q  = 1

SinQ=4/5

=> (4/5)² + Cos²Q  = 1

=> Cos²Q  = 1 - (4/5)²

=> Cos²Q   = (5² - 4²)/5²

=> Cos²Q  = 9/25

=> CosQ  = ± (3/5)

TanQ  = SinQ/CosQ

=> TanQ  =  (4/5) /(± (3/5))

=>  TanQ  =   ± 4/3

TanQ  =   ± 4/3     if  SinQ=4/5

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