 MTHH044 Trigonometric Ratios and Unit Circle Questions

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Mathematics

MTHH044

### Question Description

Please complete this assignment in full. I have 10 of the 20 questions answered, but I am not sure if they are correct. I would like to see if your answers match mine. If possible, I would prefer the assignment to be sent back in pdf form, having written on the actual document. Thanks.

### Unformatted Attachment Preview

Math | Graded Assignment | Checkup: Trigonometric Ratios and the Unit Circle Name: Date: Graded Assignment Checkup: Trigonometric Ratios and the Unit Circle Answer the following questions using what you've learned from this lesson. Write your responses in the space provided, and turn the assignment in to your teacher.  7 24  1. Show that the point  ,  is on the unit circle.  25 25  2. What is the reference angle for 11 ? Explain your thinking. 6 3. What is the reference angle for 14  ? Explain your thinking. 3 © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 1 of 4 Math | Graded Assignment | Checkup: Trigonometric Ratios and the Unit Circle  4  4. If the point P  − , y  lies on the unit circle and P is in the third quadrant, what is y? Explain.  5   2 5. If the point P  x,  lies on the unit circle and P is in the second quadrant, what is x? Explain.  3 6. What are the coordinates of the terminal point determined by  = 7 ? 6 7. Sketch a unit circle and label the terminal points corresponding to  =  3 5 7 , , , 4 4 4 4 Include the coordinates of each point. 8. Sketch a unit circle and label the terminal points corresponding to  =  5 7 11 , , , 6 6 6 6 Include the coordinates of each point. 9. Sketch a unit circle and label the terminal points corresponding to  =  2 4  5  , , , 3 3 3 3 Include the coordinates of each point. © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 2 of 4 Math | Graded Assignment | Checkup: Trigonometric Ratios and the Unit Circle 10. Sketch a unit circle and label the terminal points corresponding to  = 0,  3 , , , 2 2 2 Include the coordinates of each point.  3  11. What is tan   ? Explain your thinking.  4  12. If  is any real number, is it possible for sin  = 5 ? Why or why not? 4 13. If  is any real number, is it possible for sin  = 0.25 and cos  = 0.5 ? Why or why not?  2  14. What is csc   ? Explain your thinking.  3   11  15. What is cos   ? Explain your thinking.  3  © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 3 of 4 Math | Graded Assignment | Checkup: Trigonometric Ratios and the Unit Circle  13  16. What is sin   ? Explain your thinking.  4  17. Give an example of a real number  for which cos  is positive and sin  is negative. 18. Give an example of a real number  for which cos is negative and sin  is positive. 19. Give the coordinates of the terminal point corresponding to  = 10 . 3 20. Give the coordinates of the terminal point corresponding to  = 15 . 6 © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 4 of 4 ...
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## Final Answer Hey there!it's been a lengthy assignment but I solved it anywayhere is the solution

Math | Graded Assignment | Checkup: Trigonometric Ratios and the Unit Circle

Name:

Date:

Graded Assignment
Checkup: Trigonometric Ratios and the Unit Circle
Answer the following questions using what you've learned from this lesson. Write your responses in the
space provided, and turn the assignment in to your teacher.

 7 24 
1. Show that the point  ,
 is on the unit circle.
 25 25 
This point is on the unit circle if 𝑥 2 + 𝑦 2 = 1
7 2
24 2
49 576 625
∴( ) +( ) =
+
=
=1
25
25
625 625 625
7 24
∴ ( , ) is on the unit circle
24 25

11
? Explain your thinking.
6
This angle is in the fourth quadrant, so the reference angle is
11
1
θ𝑟𝑒𝑓 = 2π −
π= π
6
6
1
The angle between the terminal rayt and the x-axis is π

2. What is the reference angle for

6

14 
? Explain your thinking.
3
This angle is in the firth quadrant, so the reference angle is
14
2
θ𝑟𝑒𝑓 =
π − 4π = π
3
3

3. What is the reference angle for

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