Question

Sketch the angle ( = 340° in standard position to help answer the following:

a.) Angle A lies in quadrant _____degrees.
b.) A positive coterminal angle with is _____ degrees.
c.) A negative coterminal angle with O is _____degrees.
d.) The reference angle for is _____degrees.

Answer 1

a.) Angle A lies in fourth quadrant

b.) A positive coterminal angle with A is 700 degrees.

c.) A negative coterminal angle with A is -20 degrees.

d.) The reference angle for A is 20 degrees.

How to fill the blanks

Given data

angle A = 340 degrees is in standard position

a.) Angle A lies between 270 and 360 which is fourth quadrant

b.) A positive coterminal angle with A can be found by adding multiples of 360

340 + 360 = 700 degrees is a positive coterminal angle.

c.) A negative coterminal angle with A can be found by subtracting multiples of 360

340 - 360 = -20 is a negative coterminal angle.

d.) The reference angle for A is the acute angle formed between the terminal side of A and the x-axis. Since A is in the fourth quadrant, the reference angle is the angle between A and the nearest x-axis, which is

= A - 360

= | 340 - 360 |

= 20