Question

Which shows the graph of a cosine curve with amplitude 3, period pi/4 and a<0?

Answer 1

periodic functions and trigonometry practice

1. c

2. b

3. c

4. c

5. b

6. d

7. d

8. b

9. b

10. c

11. c

12. a

13. d

14. c

15. d

16. a

17. b

18. d

Answer 2

Given that you don't provide a graph, I will try to solve this problem using the data written in the question. A cosine function is given by the formula:


`y=Acos(\omega x) \\ \\ where \ A \ is \ the \ amplitude \ and \ \omega \ is \ the \ angular \ frequency`

According to the statement, the amplitude of this function is equal to
`3`. So we need to find the period that is related to
`\omega` like this:


`\omega=(2 \pi)/(T) \\ \\ \therefore \omega=(2 \pi)/((\pi)/(4))=8 \ rad/seg`

Accordingly:


`y=3cos(8x)`

So this graph is shown in the figure below. The frequency of this function is 8 times the frequency of the function
`cos(x)` and the amplitude acts as a scaling factor.