Sinusoidal Functions Flashcards

(25 cards)

1
Q

Whats the conversion for degrees to radians

A

(deg) * (π / 180)

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2
Q

Conversion for radians to degrees

A

(rad) * (180 / π)

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3
Q

Whats the sin equivalent for csc

A

1 / sinθ

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4
Q

whats the cos equivalent for sec

A

1 / cosθ

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5
Q

whats the cos/sin equivalent for cot

A

cosθ / sinθ

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6
Q

Whats the domain/range/period of a csc function

A

D = R, x ≠ kπ (k = int)
R = (- ∞, -1] U [1, ∞)
p = 2π

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7
Q

Whats the domain/range/period of a sec function

A

D = R, x ≠ kπ / 2 (k = odd int)
R = (- ∞, -1] U [1, ∞)
p = 2π

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8
Q

Whats the domain/range/period of a cot function

A

D = R, x ≠ kπ (k = int)
R = R
p = π

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9
Q

what is the equation for tan

A

sinθ / cosθ

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10
Q

Whats the domain/range of an arc sin / sin^-1 function

A

D = [-1, 1]
R = [-π/2, π/2]

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11
Q

Whats the domain/range of an arc cos / cos^-1 function

A

D = [-1, 1]
R = [0, π]

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12
Q

Whats the domain/range of an arc tan / tan^-1 function

A

D = (-∞, ∞)
R = (-π/2, π/2)

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13
Q

Whats the range of sin^-1(sin(x)) = x

A

-π/2 ≤ x ≤ π/2

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14
Q

Whats the range of sin(sin^-1(x)) = x

A

-1 ≤ x ≤ 1

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15
Q

do the sin’s cancel in: sin(sin^-1(x)) = x

A

yes

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16
Q

Whats the range of cos^-1(cos(x)) = x

A

0 ≤ x ≤ π

17
Q

Whats the range of cos(cos^-1(x)) = x

A

-1 ≤ x ≤ 1

18
Q

Whats the range of tan(tan^-1(x)) = x

A

-π/2 < x < π/2

19
Q

Whats the range of tan^-1(tan(x)) = x

A

-∞ ≤ x ≤ ∞

20
Q

On the unit circle, which portion does cos take up

21
Q

On the unit circle, which portion does sin take up

A

The right half

22
Q

On the unit circle, which portion does tan take up

A

The top half and right half

23
Q

Is tan^2θ =(tanθ)^2

24
Q

Is θ = π/4 a solution for 2sinθ - 1 = 0

A

2sin(π/4) - 1 = 0;
sin(π/4) = 1/2;
√2 / 2 ≠ 1/2;

No

25
Is θ = π/6 a solution for 2sinθ - 1 = 0
2sin(π/6) - 1 = 0; sin(π/6) = 1/2; 1/2 = 1/2; Yes