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Popular >

f(θ)=2sin^2(θ)-3sin(θ)+1

Solution

f (θ) = 2 sin^{2} (θ) - 3 sin (θ) + 1

Solution

Period : 2 π

Domain : - \infty < θ < \infty

Range : - \frac{1}{8} \leq f (θ) \leq 6

X Intercepts : (\frac{π}{2} + 2 πn, 0), (\frac{π}{6} + 2 πn, 0), (\frac{5 π}{6} + 2 πn, 0), Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Minimum (arcsin (\frac{3}{4}) + 2 πn, - \frac{1}{8}), Maximum (\frac{π}{2} + 2 πn, 0), Minimum (π - arcsin (\frac{3}{4}) + 2 πn, - \frac{1}{8}), Maximum (\frac{3 π}{2} + 2 πn, 6)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{8}, 6]

Solution steps

Periodicity of

2 sin^{2} (θ) - 3 sin (θ) + 1 : 2 π

Domain of

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

Range of

2 sin^{2} (θ) - 3 sin (θ) + 1 : - \frac{1}{8} \leq f (θ) \leq 6

Axis interception points of

2 sin^{2} (θ) - 3 sin (θ) + 1 :

X Intercepts

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

Y Intercepts

: (0, 1)

Asymptotes of

2 sin^{2} (θ) - 3 sin (θ) + 1 :

None

Extreme Points of

2 sin^{2} (θ) - 3 sin (θ) + 1 :

Minimum

(arcsin (\frac{3}{4}) + 2 πn, - \frac{1}{8}),

Maximum

(\frac{π}{2} + 2 πn, 0),

Minimum

(π - arcsin (\frac{3}{4}) + 2 πn, - \frac{1}{8}),

Maximum

(\frac{3 π}{2} + 2 πn, 6)

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Frequently Asked Questions (FAQ)

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