Vectors and Trigonometry
Components of a vector via sine and cosine.
Key idea
Components of a vector via sine and cosine.
In depth
A vector with magnitude r at angle θ has components (r cos θ, r sin θ). Adding vectors adds components. The direction of a vector comes from tan θ = y/x, adjusting for the quadrant.
Worked example
A force of 50 N at 30° above horizontal has components 43.3 N and 25 N.
Formula
Real-world uses
- Breaking a wind speed or a force into horizontal and vertical parts for engineering
Common mistake
Using the wrong function for each component.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Vectors and Trigonometry?
Components of a vector via sine and cosine. It is a topic at the advanced level in Trigonometry.
What is the formula for Vectors and Trigonometry?
The key formula is v = (|v|cosθ, |v|sinθ).
Where is Vectors and Trigonometry used in real life?
Real-world examples: Breaking a wind speed or a force into horizontal and vertical parts for engineering.
What should I learn before Vectors and Trigonometry?
Make sure you are comfortable with Bearings and Navigation, the previous topic in Trigonometry.
What is a common mistake with Vectors and Trigonometry?
Using the wrong function for each component.
How can I practise Vectors and Trigonometry?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Vectors and Trigonometry?
Move on to Resultant Forces next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.