Question

An angle whose measure is 405° is in standard position. In what quadrant does the terminal side of the angle fall?

A. Quadrant I
b. Quadrant II
c. Quadrant III
d. Quadrant IV

Answer 1

Quadrant I

405=360+45 405-360=45

405 is one complete counterclockwise rotation plus one half of an angle measuring 90 degrees counterclockwise rotation (=45)

Answer 2

Answer: The correct option is (A) Quadrant I.

Step-by-step explanation: Given that an angle whose measure is 405° is in standard position.

We are to select the quadrant in which the terminal side of the angle fall.

We know that each quadrant covers an angle of 90°, and there are four quadrants in two-dimensional plane.

So, a whole angle is equal to the sum of the angles covered by the four quadrants.

That is, a whole angle is equal to

90° + 90° + 90° + 90°

=360°.

We have

405° - 360° = 45°.

Since the terminal sides of angles measuring from 0° to 90° lies in the first quadrant.

So, the terminal side of the angle having measure 45° will also lie in the Quadrant I, because

0° < 45° < 90°.

Thus, (A) is the correct option.