Question

if tan A=4/3,find the value of sinA &cosA​

Answer 1

Answer:

tan=perpendicular/base

given that

tan=4/3

which means

perpendicular=4

base=3

Pythagoras theorem

p²+b² =hypotenuse ²

4²+3² = h²

16+9=hypotenuse ²

25= hypotenuse ²

✓25=hypotenuse

5=hypotenuse

sin=p/h

sinA=4/5

cosA=3/5

Answer 2

Answer:

tan A =4/3

We know,

tan^2A +1= sec^2 A

(4/3)^2 A +1 = sec^2 A

16/9+1 =sec^2 A

16+9/9= sec^2 A

25/9 = sec^2 A

sec A = √ 25/9

sec A = 5/3

cos A = 1/sec A

cos A = 3/5

We also know,

cos^2 A +sin^2 A= 1

sin^2A = 1 - cos ^2

sin^2A = 1 - (3/5)^2

sin^2A= 1 - 9/25

sin^2A = 25-9/25

sin^2A = 16/25

sinA = √16/25

sinA = 4/3

Step-by-step explanation:

sin A = 4/3 & cos A = 3/5