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1.The table provides various values, including all minimums and maximums, of a cosine function f (x) on the interval [0, 2π].
Angle 0 pi over 6 pi over 2 5 pi over 6 3 times pi over 2 2π
f (x) 1 0 –1 0 3 1
What is the period of the function?
A) 2 times pi over 3
B) pi over 2
C) π
D) 2π


2.On a dogleg golf hole, one golfer hits the ball 270 yards and then another 170 yards to reach the green. The angle between the two hits is equal to 100 degrees. How far would the golfer have to originally hit the ball for it to go directly to the same position on the green?
A) 150.463 yards
B) 106.746 yards
C) 343.134 yards
D) 117,740.903 yards

3. A sine function has an amplitude of 2, a period of π, and a phase shift of negative pi over 4 period What is the y-intercept of the function?
A) 2
B) 0
C)–2
D) pi over 4

Sagot :

Problem 1

Answer: D) 2pi

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Explanation:

The given table we have is

[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}\text{Angle} & 0 & \pi/6 & \pi/2 & 5\pi/6 & 3\pi/2 & 2\pi\\ \cline{1-7}f(x) & 1 & 0 & -1 & 0 & 3 & 1\\ \cline{1-7}\end{array}[/tex]

If you were to graph all those points and draw a cosine curve through them, then the function you should get is

[tex]y = 2\cos\left(x+\frac{\pi}{2}\right)+1[/tex]

The B coefficient is 1, so that leads to a period of

T = 2pi/B

T = 2pi/1

T = 2pi

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Problem 2

Answer: C) 343.134 yards

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Explanation:

Draw out a triangle with these properties

  • side a = 270
  • side b = 170
  • angle C = 100

We'll use the law of cosines to find side c

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 270^2 + 170^2 - 2*270*170*cos(100)

c^2 = 117740.902710

c = sqrt(117740.902710)

c = 343.133943

c = 343.134

=============================================

Problem 3

Answer: A) 2

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Explanation:

If you started with y = sin(x) and applied the transformations stated, then you should end up with [tex]y = 2\sin\left(2(x+\frac{\pi}{4})\right)\\\\[/tex]

From here, plug in x = 0 to find the y intercept.

[tex]y = 2\sin\left(2(x+\frac{\pi}{4})\right)\\\\y = 2\sin\left(2(0+\frac{\pi}{4})\right)\\\\y = 2\sin\left(\frac{\pi}{2}\right)\\\\y = 2*1\\\\y = 2\\\\[/tex]

ashishdwivedilVT

1) The period of the given function is [tex]2\pi[/tex].

2) Golfer has to originally hit the ball 343.1326 yards for it to go directly to the same position on the green.

1)The function satisfying the given table will be:

[tex]f(x) = 2Cos(\frac{\pi }{2} +x) +1[/tex]

or [tex]f(x) = -2Sinx +1[/tex]

What is a period of the function?

The period of the function is the minimum value of the dependent variable x after which the function will repeat itself.

For example, Sin x = Sin(2π + x)

So, 2π will be the period of the function.

Suppose the period of the given function is k

So, f(x+k) = f(x)

[tex]-2Sin(k+x) +1 = -2Sin x+1[/tex]

[tex]Sin (k+x) = Sin x\\Sin (k+x) = Sin (2\pi +x)[/tex]

[tex]k+x = 2\pi +x[/tex]

[tex]k =2\pi[/tex]

So the period of the given function is [tex]2\pi[/tex].

2) Consider the first hit as the side AB of a triangle, the second hit as the adjacent side to the first side i.e BC of a triangle. So, angle B will be equal to 100 degrees.

In order to originally hit the ball for it to go directly to the same position on the green we need to calculate AC

So, from the cosine rule

[tex]Cos B = \frac{AB^{2} +BC^{2}-AC^{2} }{2.AB.BC}[/tex]

AB =270

BC =170

B= 100°

[tex]Cos 100 = \frac{270^{2} +170^{2}-AC^{2} }{2.270.170}[/tex]

AC = 343.1326 yards

Therefore, 1) the period of the given function is [tex]2\pi[/tex].

2) Golfer has to originally hit the ball 343.1326 yards for it to go directly to the same position on the green.

To get more about the period of a function visit:

https://brainly.com/question/9718382

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