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Popular >

f(x)=5sin^2(x)-9sin(x)-2

Solution

f (x) = 5 sin^{2} (x) - 9 sin (x) - 2

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{121}{20} \leq f (x) \leq 12

X Intercepts : (- arcsin (\frac{1}{5}) + 2 π + 2 πn, 0), (π + arcsin (\frac{1}{5}) + 2 πn, 0), Y Intercepts : (0, - 2)

Asymptotes : None

Extreme Points : Minimum (arcsin (\frac{9}{10}) + 2 πn, - \frac{121}{20}), Maximum (\frac{π}{2} + 2 πn, - 6), Minimum (π - arcsin (\frac{9}{10}) + 2 πn, - \frac{121}{20}), Maximum (\frac{3 π}{2} + 2 πn, 12)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{121}{20}, 12]

Solution steps

Periodicity of

5 sin^{2} (x) - 9 sin (x) - 2 : 2 π

Domain of

5 sin^{2} (x) - 9 sin (x) - 2 : - \infty < x < \infty

Range of

5 sin^{2} (x) - 9 sin (x) - 2 : - \frac{121}{20} \leq f (x) \leq 12

Axis interception points of

5 sin^{2} (x) - 9 sin (x) - 2 :

X Intercepts

: (- arcsin (\frac{1}{5}) + 2 π + 2 πn, 0), (π + arcsin (\frac{1}{5}) + 2 πn, 0),

Y Intercepts

: (0, - 2)

Asymptotes of

5 sin^{2} (x) - 9 sin (x) - 2 :

None

Extreme Points of

5 sin^{2} (x) - 9 sin (x) - 2 :

Minimum

(arcsin (\frac{9}{10}) + 2 πn, - \frac{121}{20}),

Maximum

(\frac{π}{2} + 2 πn, - 6),

Minimum

(π - arcsin (\frac{9}{10}) + 2 πn, - \frac{121}{20}),

Maximum

(\frac{3 π}{2} + 2 πn, 12)

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Frequently Asked Questions (FAQ)

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