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Find the values of x for which `f(x) = sqrt(sin x - cos x)` is defined.

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`f(x) = sqrt(sin x - cos x)` is defined if `sin x ge cos x`.
To solve this, we draw the graphs of y = sin x and y = cos x and see where the graph of y = sin x is above the graph of y = cos x. Since the period of both functions is `2pi`, we solve for `x in [0, 2pi]` and then generalize.

From the graph, `sin x ge cos x`, for `x in [(pi)/(4), (5pi)/(4)]`.
Generalizing, we get `x in underset(n in Z) uuu [(pi)/(4) + 2npi, (5pi)/(4) + 2npi].`
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CENGAGE-GRAPHS OF TRIGONOMETRIC FUNCTIONS-Exercise
  1. Draw the graph of y = cos pix.

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

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  3. Find the values of x for which f(x) = sqrt(sin x - cos x) is defined.

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

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

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

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

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  8. Find the number of roots of the equation x sin x = 1, x in [-2pi, 0) ...

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

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

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  11. Draw the graph of the function f(x)=m a xdot{sinx ,cos2x},x in [0,2pi]...

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

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  13. The total number of solution of sin {x}= cos {x} (where {.} denotes th...

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

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

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

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

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  18. Solve :cos x le - (1)/(2).

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

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  20. Draw the graph of y = (x^(2))/(10) sin x.

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