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Popular >

f(x)=sin(x)-cos(2x)

Solution

f (x) = sin (x) - cos (2 x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{9}{8} \leq f (x) \leq 2

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

Asymptotes : None

Extreme Points : Maximum (\frac{π}{2} + 2 πn, 2), Minimum (π + arcsin (\frac{1}{4}) + 2 πn, - \frac{9}{8}), Maximum (\frac{3 π}{2} + 2 πn, 0), Minimum (- arcsin (\frac{1}{4}) + 2 π + 2 πn, - \frac{1}{4} - cos (2 (- arcsin (\frac{1}{4}) + 2 π)))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{9}{8}, 2]

Solution steps

Periodicity of

sin (x) - cos (2 x) : 2 π

Domain of

sin (x) - cos (2 x) : - \infty < x < \infty

Range of

sin (x) - cos (2 x) : - \frac{9}{8} \leq f (x) \leq 2

Axis interception points of

sin (x) - cos (2 x) :

X Intercepts

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

Y Intercepts

: (0, sin (0) - cos (2 \cdot 0))

Asymptotes of

sin (x) - cos (2 x) :

None

Extreme Points of

sin (x) - cos (2 x) :

Maximum

(\frac{π}{2} + 2 πn, 2),

Minimum

(π + arcsin (\frac{1}{4}) + 2 πn, - \frac{9}{8}),

Maximum

(\frac{3 π}{2} + 2 πn, 0),

Minimum

(- arcsin (\frac{1}{4}) + 2 π + 2 πn, - \frac{1}{4} - cos (2 (- arcsin (\frac{1}{4}) + 2 π)))

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Frequently Asked Questions (FAQ)

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