If sin θ = 12find the values of cos θ 13

1.	If sin θ = 12find the values of cos θ 13
Answer» <P>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 Given: sin θ = 12/13 To find: cos θ and tan θ Solution: sin θ = 12/13 In a right-angled triangle, sin θ = 12/13 Perpendicular (P)/ Hypotenuse (H) = 12/13 ⇒ Let P = 12k and H = 13k By using Pythagoras THEOREM, H² = P² + B² (13k)² = (12k)² + B² 169k² = 144k² + B² B² = 25k² B = 5k Now, cos θ = Base/Hypotenuse cos θ = 5k/13k ∴ cos θ = 5/13 tan θ = sin θ/cos θ tan θ = 12/13 × 13/5 ∴ tan θ = 12/5

Answer»

<P>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

Given: sin θ = 12/13

To find: cos θ and tan θ

Solution: sin θ = 12/13

In a right-angled triangle, sin θ = 12/13

Perpendicular (P)/ Hypotenuse (H) = 12/13

⇒ Let P = 12k and H = 13k

By using Pythagoras THEOREM, H² = P² + B²

(13k)² = (12k)² + B²

169k² = 144k² + B²

B² = 25k²

B = 5k

Now, cos θ = Base/Hypotenuse

cos θ = 5k/13k

∴ cos θ = 5/13

tan θ = sin θ/cos θ

tan θ = 12/13 × 13/5

∴ tan θ = 12/5

Discussion