Trigonometric Equations
- Author:
- AMBIK BARAL
Exercise 5.5
1. (a) Define trigonometric equation with example.
Solution:
An equation involving trigonometric ratios is called trigonometric equation.
For example:
(i)
(ii)
(b) What do you mean by root (solution) of the given trigonometric equation?
Solution:
The value of an unknown angle which satisfies the given trigonometric equation is known as its root or solution.
2. (a) If , what is the least positive angle in quadrant.
Solution:
In first quadrant all the trigonometric ratios are positive, so there is not any angle in the first quadrant that satisfies .
2. (b) How to find the angle in quadrant, if the least positive angle is given.
Solution:
If the least positive angle is given, then the angle in quadrant
2. (c) What are the minimum and maximum values of and
Solution:
The minimum value of and
The maximum values of and
3. Solve:
(a)
Solution:
(b)
Solution:
(c)
Solution:
(d)
Solution:
(e)
Solution:
(f )
Solution:
(g)
Solution:
(h)
Solution:
4. Solve:
(a)
Solution:
(b)
Solution:
(c)
Solution:
(d)
Solution:
(e)
Solution:
(f)
Solution:
5. (a) Solve:
Solution:
Now,
5. (b) Solve:
Solution:
Now,
5. (c) Solve:
Solution:
Now,
5. (d) Solve:
Solution:
Now,
5. (e) Solve:
Solution:
Now,
5. (f) Solve:
Solution:
6. (a) Solve:
Solution:
Now,
6. (b) Solve:
Solution:
Now,
6. (c) Solve:
Solution:
Now,
6. (d) Solve:
Solution:
6. (e) Solve:
Solution:
Now,
6. (f) Solve:
Solution:
Now,
6. (g) Solve:
Solution:
6. (h) Solve:
Solution:
7. Solve:-
(a)
Solution:
7. Solve:-
(b)
Solution:
7. Solve:-
(c)
7. Solve:-
(d)
Solution:
7. Solve:-
(e)
Solution:
7. Solve:-
(f)
Solution:
7. Solve:-
(g)
Solution:
7. Solve:-
(h)
Solution:
7. Solve:-
(i)
Solution:
7. Solve:-
(j)
Solution:
8. Solve:-
(a)
Solution:
8. Solve:-
(b)
Solution:
8. Solve:-
(c)
Solution:
8. Solve:-
(d)
Solution:
8. Solve:-
(e)
Solution:
8. Solve:-
(f)
Solution:
8. Solve:-
(g)
Solution:
8. Solve:-
(h)
Solution:
8. Solve:-
(i)
Solution:
9. Solve:-
(a)
Solution:
9. Solve:-
(b)
Solution:
9. Solve:-
(c)
Solution:
9. Solve:-
(d)
Solution:
9. Solve:-
(e)
Solution:
9. Solve:-
(f)
Solution:
9. Solve:-
(g)
Solution:
10. Solve:
Solution:
11. (a) If , find the minimum value of .
Solution:
(b)
, find .
Solution: