QuestionFind measures of a positive angle and a negative angle coterminal with radians and distinct from it.
Give the answers in simplest form.
positive angle = radians
negative angle radians
Studdy Solution
STEP 1
What is this asking?
We need to find one positive and one negative angle that are coterminal with radians, meaning they point in the same direction, but have different rotations.
Watch out!
Remember, coterminal angles share the same initial and terminal sides, but can be reached by rotating different amounts.
Don't forget to simplify your answers!
STEP 2
1. Find a positive coterminal angle.
2. Find a negative coterminal angle.
STEP 3
Alright, let's **start** with our given angle, .
Since it's negative, we'll need to add a **whole number** of full rotations to make it positive.
A full rotation is radians.
STEP 4
Let's add to our angle:
To add these, we need a **common denominator**.
We can rewrite as .
Now we have:
This is still negative!
We need to keep **adding** full rotations.
STEP 5
Let's add another , which is the same as adding another :
Still negative!
One more rotation should do it!
STEP 6
Adding another : Woohoo! This is a positive angle coterminal with our **original angle**.
STEP 7
Now, let's find a *negative* coterminal angle.
We can do this by *subtracting* from our original angle, .
STEP 8
Remember, is the same as , so we have: This is negative and distinct from our original angle, so we've found our **negative coterminal angle**!
STEP 9
Positive coterminal angle: radians Negative coterminal angle: radians
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