State the quadrant in which the terminal side of each angles lies. 480^\circ

Step-by-step explanation:

Use only a non-collapsible compass and a straight-edge (not a ruler), construct a square with sides AB.

1. Have the compass length as AB.

2. Draw a straight line XY with a straight edge of length much greater than AB.

3. Now mark a point P on XY.

4. With P as center cut an arc on line XY for Q. Now PQ = AB.

5. With P as center cut two arcs on either side of line XY.

6. With Q as center cut two arcs on either side of line XY, so that they make two points with the arcs drawn with P as center.

7. Mark those points as R and S.

8. Now join P, R, Q, S.

9. Now we have a parallelogram PRQS. PR = RQ = QS = SP parallelogram with all sides equal is a rhombus.

10. The Diagonals of the rhombus are perpendicular to each other

11. Now Draw a line UV with points R ans S.

12. Now mark the point at which RS cuts PQ as A.

13. With A as center cut an arc on UV to get the point C.

14. With A as center cut an arc on XY to get the point B.

15. With B as center cut an arc on one side of XY.

16. With C as center cut an arc which cuts the ac drawn with B as center to get the point D.

17. Now ABCD is the required Square with side AB.

or

use compass and ruler

1.

Draw a line from the left side of your paper to the right using a ruler. Draw and label two endpoints. End point A will be on the left and end point B on the right. The distance from point A and point B will be labeled r. Distance r will be the length of each side of your square. Extend the line further to the right from point B to help in finding a new line that will be perpendicular to Line AB.

2.

Draw a perpendicular line upwards from point B. Using distance r, mark and label a new end point C. This will be the second side of the square at an exact 90 degree angle.

3.

Draw an arc with end point A as the center and r as the distance using a compass. Draw a second arc using end point C as the center and r as the distance. Mark and label where these two arcs meet as point D. This is the final corner for your square.

4.

Connect end point A to point D with your ruler. Connect end point C to point D.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: