Question

If cosx = 6/ 10 then find sinx

Answer 1

Answer:

sin x = 8/10 or 4/5

Step-by-step explanation:

cos x = adj side/ hypote

=6/10

by pythagorean theorem

6^2 + y^2 = 10^2

36 + y^2 = 100

y^2 = 100 - 36

y^2 = 64

y = opposite side = root 64 = 8

sin x = opp side/ hypote

sin x = 8/10 or 4/5

Answer 2

Answer- The above question is from the chapter 'Trigonometric Functions'.

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ

Trigonometric Identites:

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

Given question: If cos x = 6/10, then find sin x.

Solution: cos x = 6/10 = 3/5

cos x is positive.

So, x can lie either in Ist or IVth quadrant.

When x lies in Ist quadrant,

sin²x + cos²x = 1

sin²x + (3/5)² = 1

sin²x + 9/25 = 1

sin²x = 1 - 9/25 = (25 - 9)/25 = 16/25

sin x = ±√16/25

sin x = 4/5 (∵ in Ist quadrant, all T-Ratios are positive.)

When x lies in IVth quadrant,

sin²x + cos²x = 1

sin²x + (3/5)² = 1

sin²x + 9/25 = 1

sin²x = 1 - 9/25

sin²x = 16/25

sin x = ±√16/25

sin x = - 4/5 (∵ sin θ is negative in IVth quadrant.)

∴sin x can be 4/5 or - 4/5.