If sin θ = 12/13 , then find the value of cos θ and tan θ.
Answers
Answer- The above question is from the chapter 'Trigonometric Ratios'.
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
∴ cos θ = 5/13 and tan θ = 12/5
Answer:
- sin a =12/13
- sin a = p/h
- p=12
- h=13
- according to Pythagoras thereoum
- h^2=p^2+b^2
- b^2=h^2-p^2