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Popular >

y=1+sin^2(x)-2cos^3(x)

Solution

y = 1 + sin^{2} (x) - 2 cos^{3} (x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq 3

X Intercepts : (0.53924 \dots + 6.28318 \dots n, 0), (5.74393 \dots + 6.28318 \dots n, 0), Y Intercepts : (0, - 1)

Asymptotes : None

Extreme Points : Minimum (2 πn, - 1), Maximum (\frac{π}{2} + 2 πn, 2), Minimum (arccos (- \frac{1}{3}) + 2 πn, \frac{53}{27}), Maximum (π + 2 πn, 3), Minimum (- arccos (- \frac{1}{3}) + 2 π + 2 πn, \frac{53}{27}), Maximum (\frac{3 π}{2} + 2 πn, 2)

+1

Solution steps

Periodicity of

1 + sin^{2} (x) - 2 cos^{3} (x) : 2 π

Domain of

1 + sin^{2} (x) - 2 cos^{3} (x) : - \infty < x < \infty

Range of

1 + sin^{2} (x) - 2 cos^{3} (x) : - 1 \leq f (x) \leq 3

Axis interception points of

1 + sin^{2} (x) - 2 cos^{3} (x) :

X Intercepts

: (0.53924 \dots + 6.28318 \dots n, 0), (5.74393 \dots + 6.28318 \dots n, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

1 + sin^{2} (x) - 2 cos^{3} (x) :

None

Extreme Points of

1 + sin^{2} (x) - 2 cos^{3} (x) :

Minimum

(2 πn, - 1),

Maximum

(\frac{π}{2} + 2 πn, 2),

Minimum

(arccos (- \frac{1}{3}) + 2 πn, \frac{53}{27}),

Maximum

(π + 2 πn, 3),

Minimum

(- arccos (- \frac{1}{3}) + 2 π + 2 πn, \frac{53}{27}),

Maximum

(\frac{3 π}{2} + 2 πn, 2)

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Frequently Asked Questions (FAQ)

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