Precalc test 2 fill in the blank

The value of sin x (increases/decreases) ________ on (0, π/2) and (increases/decreases) ________ on (π/2, π)

increases, decreases

For y = cosx, the domain is

(-∞, ∞)

For y = sinx, the domain is

(-∞, ∞)

(sinx) On the interval [0, 2π], the x-intercepts are

(0, 0), (π, 0), (2π, 0)

(cosx) On the interval [0, 2π], the maximum points are

(0, 1), (2π, 1)

Over what interval(s) is taken between 0 and 2π is the graph of y = sinx increasing?

(0, π/2) ∪ (3π/2, 2π)

(sinx) On the interval [0, 2π], the minimum point is

(3π/2, -1)

(cosx) On the interval [0, 2π], the minimum point is

(π, -1)

(cosx) On the interval [0, 2π], the x-intercepts are

(π/2, 0), (3π/2, 0)

(sinx) On the interval [0, 2π], the maximum point is

(π/2, 1)

Over what interval(s) between 0 and 2π is the graph of y = sinx decreasing?

(π/2, 3π/2)

For y = cosx, the amplitude is

1

For y = sinx, the amplitude is

1

For y = cosx, the period is

2π

For y = sinx, the period is

2π

Given y = Asin (Bx-C) + D or y = Acos (Bx-C) + D, the period is equal to

2π/B

Given y = Asin (Bx-C) + D or y = Acos (Bx-C) + D, the phase shift is

C/B

Given y = Asin (Bx-C) + D or y = Acos (Bx-C) + D, the vertical shift is

D

For y = cosx, the range is

[-1, 1]

For y = sinx, the range is

[-1, 1]

The value of cos x (increases/decreases) ________ on (0, π/2) and (increases/decreases) ________ on (π/2, π)

decreases, decreases

The cosine function is an (even/odd) _________ function because cos(-x) is equal to cos(x)

even

Given y = sin(Bx) and y = cos(Bx), for B > 1, the period is (less than/greater than) _______ 2π. If 0 < B < 1, the period is (less than/greater than) ________ 2π.

less than 2π, greater than 2π

The sine function is an (even/odd) ________ function because sin(-x) equals -sin(x)

odd

The sine function is symmetric to

the origin

The cosine function is symmetric to the (x/y) ____ axis.

y

Given B > 0, how would the equation y = Asin (-Bx-C) + D be rewritten to obtain a positive coefficient on x?

y = -Asin (Bx+C) + D

Given B > 0, how would the equation y = Acos (-Bx-C) + D be rewritten to obtain a positive coefficient on x?

y = Acos (Bx+C) + D

Given y = Asin (Bx-C) + D or y = Acos (Bx-C) + D, for B > 0 the amplitude is

|A|

The graph of y = sin x and y = cos x differ by a horizontal shift of _______ units

π/2