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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : sin (2 (π - arcsin (\frac{33 - 1}{8}))) + cos (π - arcsin (\frac{33 - 1}{8})) \leq f (x) \leq sin (2 arcsin (\frac{33 - 1}{8})) + 1 - \frac{17 - 33}{32}

X Intercepts : (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0), (\frac{7 π}{6} + 2 πn, 0), (\frac{11 π}{6} + 2 πn, 0), Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum arcsin (\frac{33 - 1}{8}) + 2 πn, sin (2 arcsin (\frac{33 - 1}{8})) + 1 - \frac{17 - 33}{32}, Minimum (π - arcsin (\frac{33 - 1}{8}) + 2 πn, sin (2 (π - arcsin (\frac{33 - 1}{8}))) + cos (π - arcsin (\frac{33 - 1}{8}))), Maximum (π + arcsin (\frac{1 + 33}{8}) + 2 πn, sin (2 (π + arcsin (\frac{1 + 33}{8}))) + cos (π + arcsin (\frac{1 + 33}{8}))), Minimum (- arcsin (\frac{1 + 33}{8}) + 2 π + 2 πn, sin (2 (- arcsin (\frac{1 + 33}{8}) + 2 π)) + cos (- arcsin (\frac{1 + 33}{8}) + 2 π))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : sin (2 (π - arcsin (\frac{33 - 1}{8}))) + cos (π - arcsin (\frac{33 - 1}{8})), sin (2 arcsin (\frac{33 - 1}{8})) + 1 - \frac{17 - 33}{32}

Solution steps

Periodicity of

sin (2 x) + cos (x) : 2 π

Domain of

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

Range of

sin (2 x) + cos (x) : sin (2 (π - arcsin (\frac{33 - 1}{8}))) + cos (π - arcsin (\frac{33 - 1}{8})) \leq f (x) \leq sin (2 arcsin (\frac{33 - 1}{8})) + 1 - \frac{17 - 33}{32}

Axis interception points of

sin (2 x) + cos (x) :

X Intercepts

: (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0), (\frac{7 π}{6} + 2 πn, 0), (\frac{11 π}{6} + 2 πn, 0),

Y Intercepts

: (0, 1)

Asymptotes of

sin (2 x) + cos (x) :

None

Extreme Points of

sin (2 x) + cos (x) :

Maximum

arcsin (\frac{33 - 1}{8}) + 2 πn, sin (2 arcsin (\frac{33 - 1}{8})) + 1 - \frac{17 - 33}{32},

Minimum

(π - arcsin (\frac{33 - 1}{8}) + 2 πn, sin (2 (π - arcsin (\frac{33 - 1}{8}))) + cos (π - arcsin (\frac{33 - 1}{8}))),

Maximum

(π + arcsin (\frac{1 + 33}{8}) + 2 πn, sin (2 (π + arcsin (\frac{1 + 33}{8}))) + cos (π + arcsin (\frac{1 + 33}{8}))),

Minimum

(- arcsin (\frac{1 + 33}{8}) + 2 π + 2 πn, sin (2 (- arcsin (\frac{1 + 33}{8}) + 2 π)) + cos (- arcsin (\frac{1 + 33}{8}) + 2 π))

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Frequently Asked Questions (FAQ)

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