# AP Physics: Vectors and Trigonometry

In your prep for the AP Physics exam, make sure you have a solid understanding of fundamental topics like vectors and trigonometry. For a brush-up, check out the notes and practice questions below!

### Objective 1

Describe the sine and cosine functions using the unit circle

#### Objective 1 Notes

• The unit circle is a circle with radius = 1, centered at point (0, 0)—the origin
• To use the unit circle, draw a radius from the origin to the circle at some angle theta, θ
• The rise:
• Where the radius and the circle intersect, draw a line straight down to the x-axis
• This line is called the rise or the opposite
• Its length is sin(θ)
• The run:
• Where the rise meets the x-axis, draw a line along the x-axis back to the origin
• This line is called the run or the adjacent
• Its length is cos(θ)
• The unit circle is a simple tool for understanding and remembering the relationships between common angles, sine values, and cosine values

### Objective 2

#### Objective 2 Notes

• Angles may be measured in degrees or radians, where radians are the SI unit for angles
• Radians are defined using the concept of pi:
• Pi, π, is the ratio of a circle’s circumference to its diameter
• You can imagine diameter as a line passing straight from the right edge of the circle to the left edge of the circle
• So a “π angle” is actually a straight line
• Radians and π are very useful for reporting angles as fractions:
• 2π radians make one complete circle
• Multiply 2π by any fraction, and you find that fraction of a circle

### Objective 3

Differentiate between vectors and scalars

#### Objective 3 Notes

• In physics, many numbers have both magnitude and net direction
• These numbers, with magnitude and net direction, are called vectors
• A vector’s direction is usually given as an angle relative to the x-axis, or relative to another vector
• The magnitude of a vector is just a number
• All vectors in physics can be given in SI units
• In physics, some numbers do not have a net direction; these are called scalars
• A vector is usually represented as an arrow
• The length of the arrow represents the vector’s magnitude
• The direction of the arrow is the same as the vector’s direction
• Often, a vector’s direction is ignored, so many vector quantities have a scalar version

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