Math  /  Trigonometry

QuestionQuestion 8 (1 point) Determine the exact degree measure for π6\frac{\pi}{6}. 6060^{\circ} 2020^{\circ} 3030^{\circ} 4545^{\circ}

Studdy Solution

STEP 1

What is this asking? We need to convert an angle from radians to degrees.
Specifically, we want to know how many degrees are in π6\frac{\pi}{6} radians. Watch out! Remember that radians and degrees are just two different ways of measuring the same thing – angles!
Don't mix them up!

STEP 2

1. Set up the conversion
2. Calculate the result

STEP 3

We know that a full circle is 2π2\pi radians, which is also equal to 360360 degrees.
This gives us the **key conversion factor**: 2π radians=360 degrees 2\pi \text{ radians} = 360 \text{ degrees}

STEP 4

To make our conversion easier, let's figure out how many degrees are in **1 radian**.
We can do this by dividing both sides of our equation by 2π2\pi: 2π2π radians=3602π degrees \frac{2\pi}{2\pi} \text{ radians} = \frac{360}{2\pi} \text{ degrees} 1 radian=180π degrees 1 \text{ radian} = \frac{180}{\pi} \text{ degrees}

STEP 5

Now, we want to convert π6\frac{\pi}{6} radians to degrees.
We can multiply both sides of the equation in 2.1.2. by π6\frac{\pi}{6} to get: π61 radian=π6180π degrees \frac{\pi}{6} \cdot 1 \text{ radian} = \frac{\pi}{6} \cdot \frac{180}{\pi} \text{ degrees}

STEP 6

Let's simplify the right side of the equation from 2.1.3.
We have π\pi in the numerator and denominator, so we can divide to one: π6 radians=π6180π degrees \frac{\pi}{6} \text{ radians} = \frac{\pi}{6} \cdot \frac{180}{\pi} \text{ degrees} π6 radians=1806 degrees \frac{\pi}{6} \text{ radians} = \frac{180}{6} \text{ degrees}

STEP 7

Now, we just need to divide 180180 by 66: π6 radians=1806 degrees \frac{\pi}{6} \text{ radians} = \frac{180}{6} \text{ degrees} π6 radians=30 degrees \frac{\pi}{6} \text{ radians} = \textbf{30} \text{ degrees}

STEP 8

So, π6\frac{\pi}{6} radians is equal to **30** degrees!

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord