A Level Mathematics Year 2

A Level Mathematics Year 2 - Radians

Created by

@MotivatedWendigo5363

Study Notes

For ( \frac{\pi}{6} ) (30°):
- ( \sin \frac{\pi}{6} = \frac{1}{2} )
- ( \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2} )
- ( \tan \frac{\pi}{6} = \frac{1}{\sqrt{3}} )
For ( \frac{\pi}{3} ) (60°):
- ( \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} )
- ( \cos \frac{\pi}{3} = \frac{1}{2} )
- ( \tan \frac{\pi}{3} = \sqrt{3} )
For ( \frac{\pi}{4} ) (45°):
- ( \sin \frac{\pi}{4} = \frac{\sqrt{2}}{2} )
- ( \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2} )
- ( \tan \frac{\pi}{4} = 1 )

Arc length formula: ( l = r\theta )
- ( l ) = arc length
- ( r ) = radius of the sector
- ( \theta ) = angle in radians

Area of a sector formula: ( \text{Area} = \frac{1}{2} r^2 \theta )
- Applies to both full and minor sectors.

For problems involving arcs or sectors, identify the radius and angle to utilize the formulas for arc length and area effectively.
Practice with sector problems, such as finding lengths of paths or perimeters involving triangles with angles in radians, to reinforce understanding.

Understanding the shape and characteristics of the sine and cosine graphs is essential.
- Graphs will oscillate between -1 and 1, with specific key points at intervals defined by ( \pi ) and ( 2\pi ).

Engage with exercises that involve converting units, determining exact trigonometric values, and solving for arc lengths and areas in various contexts to build proficiency.