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Write the equivalent (piecewise) definit...

Write the equivalent (piecewise) definition of `f(x)=sgn(sinx)dot`

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`f(x) = sgn (sin x) = {{:(-1",", sin x lt 0),(0",", sin x = 0),(1",", sin x gt 0):}`
` = {{:(-1",", x in ((2n + 1) pi"," (2n + 2)pi)),(0",", x = npi"," n in Z),(1",", x in ((2npi)","(2n + 1)pi)):}`
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CENGAGE-GRAPHS OF TRIGONOMETRIC FUNCTIONS-Exercise
  1. Write the equivalent (piecewise) definition of f(x)=sgn(sinx)dot

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  2. Draw the graph of y = " cosec "^(2) x - cot^(2) x. Is f(x) periodic ? ...

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  3. Draw the graph of y = cos pix.

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  4. Draw the graph of y = cos^(2)x.

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  5. Find the value of x for which f(x)=sqrt(sinx-cosx) is defined, x in [0...

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  6. Draw the graph of y = tan^(2) x.

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  7. Draw the graph of y = sin x + cos x, x in [0, 2pi].

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  8. Draw the graph of y = [cos x], x in [0, 2pi], where [*] represents the...

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  9. Draw the graph of y = sin pisqrt(x).

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  10. The number of roots of the equation xsinx=1,x in [-2pi,0)uu(0,2pi) is ...

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  11. Evaluate : [lim(x to 0) (tan x)/(x)], where [*] represents the greates...

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  12. For f(x) = sin x - x^(2) + 1, check weather the function is increasing...

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  13. Draw the graph of the function f(x)=max dot {(sinx ,cos2x)},x in [0,2p...

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  14. Draw the graph of y = cos x, x in [0, 2pi], where [*] denotes the gre...

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  15. The total number of solution of sin{x}=cos{x} (where {} denotes the fr...

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  16. Draw the graph of f(x) = |tan x| + |cot x|.

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  17. Find the number of solutions to cos x = (x)/(10), x gt 0.

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  18. The number of solutions of tanx-m x=0,m >1, in (-pi/2,pi/2) is 1 (b) 2...

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  19. Find the number of solutions to log(e) |sin x| = -x^(2) + 2x in [-(pi)...

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  20. Solve cos x = 1/2.

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  21. Prove that the least positive value of x , satisfying tanx=x+1, lies i...

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