Question

15. The graph of which trigonometric function(s) include the point (0,2)? Select all that apply. (3 points) y = cos x + 1 y = 2 cos x y = sin x + 1 y = tan x + 1 f(x) = sin(x+y)+1 16. The data in the table represents the average number of daylight hours each month in Springfield in 2015, rounded to the nearest quarter-hour. (4 points) Month Hours January 9.5 February 10.5 March 12 April 13.25 May 14.5 June 115 July 14.75 August 13.75 September 12.5 October 11.0 November 9.75 December 9.25 Write an equation that best models the data. What is the expected number of daylight hours in March 2020? Explain. (1 point) 17. A statistician is analyzing data to find a model. She has determined the following characteristics of the data. Which characteristic of the data defines the period? The initial value is 5. All of the values are negative. The difference between the maximum and minimum values is 10 The data repeats every 4 minutes. 18. Explain why domain restrictions for inverse trigonometric functions are necessary. (4 points)

Answer 1

(15) Given point is (0,2)=(x,y)

Options :

(a) y=cosx+1

If the point (0,2) lies on the given curve, then it should satisfy the given point.

Plug x= 0 in the given equation, the if we get y value as 2, then the +1=point lies on the given equation.

y=cosx+1

y=cos0+1

= 1+1

y=2

So we got y=2

So (0,2) lies on y=cosx+1

(0,2) lies on y=cosx+1

(b) y=2cosx

Plug x=0

y=2cos0

y=2(1)

y=2

So (0,2) lies on y=2cosx

(0,2) lies on y=2cosx

(c) y=sinx+1

Plug x=0

y=sin0+1

= 0+1

y=1

we did not get y=2

So (0,2) does not lie on y=sinx+1

so this is not the right answer.

(d)

y=tanx+1

Plug x=0

y=tan0+1

= 0+1

y=1

we did not get y=2

So (0,2) does not lie on y=tanx+1

so this is not the right answer.

(e)

f(0) = sin(+ )+1

Plug x=0

f(0) = sin(0+ ) +1

I + us = (x)}

f(1) = 1+1

f(1) = 2

y=2

So (0,2) lies on the given f(x)

(0,2) lies on    f(0) = sin(+ )+1