π/4 radians = 45°
Further explanation
The basic formula that need to be recalled is:
Circular Area = π x R²
Circle Circumference = 2 x π x R
where:
R = radius of circle
The area of sector:
[tex]\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}[/tex]
The length of arc:
[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]
Let us now tackle the problem!
This problem is about conversion unit of angles
Remember that :
[tex]\large {\boxed {1 \pi ~ \text{radians} = 180^o} }[/tex]
[tex]\frac{\pi}{4} = \frac{1}{4} \times 180^o = \boxed {45^o}[/tex]
Another Example:
[tex]\frac{\pi}{6} = \frac{1}{6} \times 180^o = \boxed {30^o}[/tex]
[tex]\frac{\pi}{3} = \frac{1}{3} \times 180^o = \boxed {60^o}[/tex]
[tex]\frac{\pi}{2} = \frac{1}{2} \times 180^o = \boxed {90^o}[/tex]
[tex]\frac{3\pi}{2} = \frac{3}{2} \times 180^o = \boxed {270^o}[/tex]
[tex]\frac{3\pi}{4} = \frac{3}{4} \times 180^o = \boxed {135^o}[/tex]
[tex]\frac{4\pi}{3} = \frac{4}{3} \times 180^o = \boxed {240^o}[/tex]
Learn more
- Calculate Angle in Triangle : https://brainly.com/question/12438587
- Periodic Functions and Trigonometry : https://brainly.com/question/9718382
- Trigonometry Formula : https://brainly.com/question/12668178
Answer details
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area , Radian , Degree , Unit , Conversion
