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Popular >

y(θ)= pi/2 sin(θ)-cos(θ)

Solution

y (θ) = \frac{π}{2} sin (θ) - cos (θ)

Solution

Period : 2 π

Domain : - \infty < θ < \infty

Range : \frac{π}{2} sin (- arctan (\frac{π}{2}) + 2 π) - cos (- arctan (\frac{π}{2}) + 2 π) \leq f (θ) \leq \frac{π}{2} sin (- arctan (\frac{π}{2}) + π) - cos (- arctan (\frac{π}{2}) + π)

X Intercepts : (arctan (\frac{2}{π}) + 2 πn, 0), (arctan (\frac{2}{π}) + π + 2 πn, 0), Y Intercepts : (0, - 1)

Asymptotes : None

Extreme Points : Maximum (- arctan (\frac{π}{2}) + π + 2 πn, \frac{π}{2} sin (- arctan (\frac{π}{2}) + π) - cos (- arctan (\frac{π}{2}) + π)), Minimum (- arctan (\frac{π}{2}) + 2 π + 2 πn, \frac{π}{2} sin (- arctan (\frac{π}{2}) + 2 π) - cos (- arctan (\frac{π}{2}) + 2 π))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{π}{2} sin (- arctan (\frac{π}{2}) + 2 π) - cos (- arctan (\frac{π}{2}) + 2 π), \frac{π}{2} sin (- arctan (\frac{π}{2}) + π) - cos (- arctan (\frac{π}{2}) + π)]

Solution steps

Periodicity of

\frac{π}{2} sin (θ) - cos (θ) : 2 π

Domain of

\frac{π}{2} sin (θ) - cos (θ) : - \infty < θ < \infty

Range of

\frac{π}{2} sin (θ) - cos (θ) : \frac{π}{2} sin (- arctan (\frac{π}{2}) + 2 π) - cos (- arctan (\frac{π}{2}) + 2 π) \leq f (θ) \leq \frac{π}{2} sin (- arctan (\frac{π}{2}) + π) - cos (- arctan (\frac{π}{2}) + π)

Axis interception points of

\frac{π}{2} sin (θ) - cos (θ) :

X Intercepts

: (arctan (\frac{2}{π}) + 2 πn, 0), (arctan (\frac{2}{π}) + π + 2 πn, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

\frac{π}{2} sin (θ) - cos (θ) :

None

Extreme Points of

\frac{π}{2} sin (θ) - cos (θ) :

Maximum

(- arctan (\frac{π}{2}) + π + 2 πn, \frac{π}{2} sin (- arctan (\frac{π}{2}) + π) - cos (- arctan (\frac{π}{2}) + π)),

Minimum

(- arctan (\frac{π}{2}) + 2 π + 2 πn, \frac{π}{2} sin (- arctan (\frac{π}{2}) + 2 π) - cos (- arctan (\frac{π}{2}) + 2 π))

Popular Examples

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Frequently Asked Questions (FAQ)

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