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Popular >

y=cos(3x-6)cos(3x+6)

Solution

y = cos (3 x - 6) cos (3 x + 6)

Solution

Period : \frac{π}{3}

Domain : - \infty < x < \infty

Range : cos (\frac{π}{2} - 6) cos (\frac{π}{2} + 6) \leq f (x) \leq cos^{2} (6)

X Intercepts : (2 - \frac{π}{2} + \frac{πn}{3}, 0), (2 - \frac{π}{2} + \frac{πn}{3}, 0), (- 2 + \frac{5 π}{6} + \frac{πn}{3}, 0), Y Intercepts : (0, cos (3 \cdot 0 - 6) cos (3 \cdot 0 + 6))

Asymptotes : None

Extreme Points : Maximum (\frac{π}{3} n, cos^{2} (6)), Minimum (\frac{π}{6} + \frac{π}{3} n, cos (\frac{π}{2} - 6) cos (\frac{π}{2} + 6))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [cos (\frac{π}{2} - 6) cos (\frac{π}{2} + 6), cos^{2} (6)]

Solution steps

Periodicity of

cos (3 x - 6) cos (3 x + 6) : \frac{π}{3}

Domain of

cos (3 x - 6) cos (3 x + 6) : - \infty < x < \infty

Range of

cos (3 x - 6) cos (3 x + 6) : cos (\frac{π}{2} - 6) cos (\frac{π}{2} + 6) \leq f (x) \leq cos^{2} (6)

Axis interception points of

cos (3 x - 6) cos (3 x + 6) :

X Intercepts

: (2 - \frac{π}{2} + \frac{πn}{3}, 0), (2 - \frac{π}{2} + \frac{πn}{3}, 0), (- 2 + \frac{5 π}{6} + \frac{πn}{3}, 0),

Y Intercepts

: (0, cos (3 \cdot 0 - 6) cos (3 \cdot 0 + 6))

Asymptotes of

cos (3 x - 6) cos (3 x + 6) :

None

Extreme Points of

cos (3 x - 6) cos (3 x + 6) :

Maximum

(\frac{π}{3} n, cos^{2} (6)),

Minimum

(\frac{π}{6} + \frac{π}{3} n, cos (\frac{π}{2} - 6) cos (\frac{π}{2} + 6))

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Frequently Asked Questions (FAQ)

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