1)Find the amplitude of y=6cos4theta

A)3/2
B)6
C)4
D)pi/2
I chose B

2)Find the period of y=tan5theta
A)10pi
B)2pi/5
C)5pi
D)pi/5
I chose D

3)Find the phase shift of y=sin(theta-3pi/4).
A)3pi/4
B)-3pi/4
C)4pi/3
D)-4pi/3
I chose A

4)Find the vertical shift of y=-4sec theta+7.
A)-4
B)-7
C)7
D)4
I chose C

5)Find sec theta if tan theta=1/4 and 180 degrees<theta<270 degrees.
A)square root of 15/4
B)-square root of 15/4
C)square root of 17/4
D)-square root of 17/4
I chose C

In #5, the angle is in the third quadrant, so the cosine, and hence the secant, is negative.

sec theta = (-√17)/4

are the rest ok?

yes

1) To find the amplitude of the function y = 6cos(4θ), we can use the formula for the amplitude of a cosine function, which is given by |A|, where A is the coefficient of the cosine term.

In this case, the coefficient of the cosine term is 6. Therefore, the amplitude is |6| = 6.

The correct answer is B) 6.

2) To find the period of the function y = tan(5θ), we can use the formula for the period of a tangent function, which is given by π/|B|, where B is the coefficient of the θ term.

In this case, the coefficient of the θ term is 5. Therefore, the period is π/|5| = π/5.

The correct answer is D) π/5.

3) To find the phase shift of the function y = sin(θ - 3π/4), we can compare it to the standard form of a sine function, which is y = sin(θ - φ), where φ is the phase shift.

By comparing the given function to the standard form, we can see that the phase shift is 3π/4.

The correct answer is A) 3π/4.

4) To find the vertical shift of the function y = -4sec(θ) + 7, we can use the formula for the vertical shift of a secant function, which is given by C, where C is the constant term.

In this case, the constant term is 7. Therefore, the vertical shift is 7.

The correct answer is C) 7.

5) To find sec(θ) given tan(θ) = 1/4 and 180 degrees < θ < 270 degrees, we can use the fact that sec(θ) is the reciprocal of cos(θ). We can use the given information to find cos(θ) first.

We are given tan(θ) = 1/4, which means that the ratio of the opposite side to the adjacent side in a right triangle with angle θ is 1/4. Since θ is in the third quadrant (180 degrees < θ < 270 degrees), the adjacent side is negative and the opposite side is positive.

Using the Pythagorean theorem, we can find the hypotenuse:
(hypotenuse)^2 = (opposite side)^2 + (adjacent side)^2
(hypotenuse)^2 = (1)^2 + (-4)^2
(hypotenuse)^2 = 1 + 16
(hypotenuse)^2 = 17

Taking the square root of both sides, we get:
hypotenuse = sqrt(17)

Now, since sec(θ) = 1/cos(θ), we can find sec(θ) by taking the reciprocal of cos(θ):
sec(θ) = 1 / cos(θ) = 1 / (sqrt(17) / sqrt(17)) = sqrt(17) / 1 = sqrt(17)

The correct answer is C) sqrt(17)/4.