Question

8. If cotA=
7
then find the value of sin A.
24​

Answer 1

Answer:

given that 24cotA=7

⇒cotA=

7

24

as cot { A } is positive then the angle A must be in either first quadrant or third quadrant

⇒sinA has 2 values one positive and one negative

in a triangle cotA=

oppositeside

adjacentside

therfore adjacentside=24,oppositeside=7

hypotenuse=

(adjacentside)

2

+(oppositeside)

2

=

24

2

+7

2

=25

therefore sinA=

hypotenuse

oppositeside

=

25

7

as sin { A } is positive and negative

therefore sinA=+

25

7

or−

25

7

.

Answer 2

Explanation:

cotA=7

1/cotA=tanA

tanA=1/7

sina=2tanA/1-tan^2A

sinA=2(1/7)/1-(1/7)^2

sinA=(2/7)/1-1/49

sinA=(2/7)/(48/49)

sinA=7/24