Question

What is a positive coterminal angle to 403° that is between 500° and 1000° and a negative coterminal angle to 403° that is between −500° and 0°?

What is the value of arccos(−0.32) as a decimal to the nearest hundredth of a degree?

Answer 1

coterminal angle can be found by adding or subtracting 360°

so 403+360 = 763°

and 403-360-360 = -317°



arccos(−0.32) = 108.66 degree

Answer 2

Positive co-terminal = 763°

Negative co-terminal = -317°

arccos(-0.32)=108.66°

Explanation:

We are given an angle 403°

We need to find Positive co-terminal of angle 403° that is between 500° and 1000°

For positive co-terminal angle add 360°

Positive co-terminal of 403° ⇒ 403+360 ⇒ 763°

500° ≤ 763° ≤ 1000°

Therefore, 763° is positive co-terminal angle of 403° between 500° and 1000°

For negative co-terminal angle subtract 360°

Negative co-terminal of 403° ⇒ 403-360 ⇒ 43°

But 43° is not lie between -500° and 0°

So, we subtract 360° again

Negative co-terminal of 403° ⇒ 43°-360° ⇒ -317°

-500° ≤ -317° ≤ 0°

Therefore, -317° is negative co-terminal of 403° between -500° and 0°

# We need to find the value of arccos(−0.32) as a decimal to the nearest hundredth of degree.

Using calculator to find the inverse of cos at -0.32

Therefore, arccos(−0.32)=108.66°