tanθ increases faster than sinθ as θ increases. Write ‘True’ or ‘False’ and justify your answer
Solution:
We have to determine if tanθ increases faster than sinθ as θ increases.
Considering different cases in first quadrant,
sin 0° = 0
sin 30° = 1/2 = 0.5
sin 45° = 1/√2 = 1/1.414 = 0.707
sin 60° = √3/2 = 1.732/2 = 0.866
sin 90° = 1
tan 0° = 0
tan 30° = 1/√3 = 1/1.732 = 0.577
tan 45° = 1
tan 60° = √3 = 1.732
tan 90° = not defined
We observe that, as θ increases, tanθ increases faster than sinθ.
✦ Try This: If tan θ = 4/5, find cos θ - sin θ
Given, tan θ = 4/5
We have to find the value of (cos θ - sin θ)/(cos θ + sin θ)
We know that tan A = sin A/cos A
Here, sin θ = 4
cos θ = 5
So, cos θ - sin θ = 5 - 4 = 1
cos θ + sin θ = 5 + 4 = 9
(cos θ - sin θ)/(cos θ + sin θ) = 1/9
Therefore, (cos θ - sin θ)/(cos θ - sin θ) = 1/9
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Sample Problem 3
tanθ increases faster than sinθ as θ increases. Write ‘True’ or ‘False’ and justify your answer
Summary:
The ratio of the length of the opposite side to that of the adjacent side in any right-angled triangle is said to be the tan function. The statement “tanθ increases faster than sinθ as θ increases” is true
☛ Related Questions:
visual curriculum