Question

Given the polar coordinates 8∠43.7°, what is the equivalent polar coordinate with a negative angle?

a. 8∠- 43.7°                 b. 8∠316.3°

c. 8∠- 316.3°               d. -8∠- 316.3°

Answer 1

Equivalent Angles :

There are more than one way to arrive at the same angle.

For nagative angles, just add 360 degrees.For positive angles add nagative 360 degrees to find the equivalent angle.

So, basically we can either move clockwise or counterclockwise to arrive at the same angle.

.

Given : The polar coordinates .

→ In this problem, we are told to work in degrees.

→ Here r = 8 ( > 0), so we can use the formula, i.e.

→ We want an angle that is negative that will lead us to the equivalent point.

→ We are allowed to add or subtract a and that won't change our problem.

→ So, We can do .

→ This is an equivalent angle.

→ So, the equivalent polar coordinates with an negative angle is .

→The right choice is c .