Question

Period of f(x).-Sinx+ |sin x| is​

Answer 1

Answer:

Step-by-s2π

For example, f(x) = sin(x), B = 1, so the period is 2πtep explanation:

Answer 2

Answer :

2π

Note :

• Periodic function : A periodic function is a function that repeats its values at regular intervals . Eg : Trigonometric functions (Circular functions) .
• If f(x) is a periodic function , then f(x) = f(x+P) , where P is the least positive real number called its period .

Functions → Period

sinx , cosx → 2π

tanx , cotx → π

secx , cosecx → 2π

|All T.F.| → π

(All T.F.)² → π

|sinx + cosx| → π

|tanx + cotx| → π

|secx + cosecx| → π

• If P is the period of the function f(x) , then the period of the function f(ax+b) will be P/|a| .
• If P1 and P2 are the periods of the functions f(x) and g(x) respectively , then the period of function f(x) + g(x) will be given as , P = LCM(P1 , P2) .

Solution :

• Given : f(x) = sinx + |sinx|
• To find : Period of f(x)

We know that ,

The period of sinx is 2π = P1 (say)

Also ,

The period of |sinx| is π = P2 (say)

Thus ,

The period of the given function f(x) = sinx + |sinx| will be given as ;

=> P = LCM(P1 , P2)

=> P = LCM(2π , π)

=> P = 2π

Hence ,

Required answer is 2π .