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Home » Show that the function given by f(x)=sinx is (a) strictly increasing (0,pi/2) (b) strictly decreasing (pi/2,pi) in (c) neither increasing nor decreasing in (0,pi)
Show that the function given by f(x)=sinx is (a) strictly increasing (0,pi/2) (b) strictly decreasing (pi/2,pi) in (c) neither increasing nor decreasing in (0,pi)
Applications of Derivatives | CBSE | Class 12 | Exercise 6.2 | Maths | NCERT
Show that the function given by f(x)=sinx is (a) strictly increasing (0,pi/2) (b) strictly decreasing (pi/2,pi) in (c) neither increasing nor decreasing in (0,pi)

 Given: 

 

(a) Since,  > 0, i.e., positive in first quadrant, i.e., in 

Therefore,  is strictly increasing in 

(b) Since,  < 0, i.e., negative in second quadrant, i.e., in 

Therefore,  is strictly decreasing in 

(c) Since  > 0, i.e., positive in first quadrant, i.e., in  and  < 0, i.e., negative in second quadrant, i.e., in  and .

   does not have the same sign in the interval 

Therefore,  is neither increasing nor decreasing in 

i

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