Resultant Forces
Add vectors using trigonometry.
Key idea
Add vectors using trigonometry.
In depth
The resultant is the single force equal to the vector sum of all the forces. Resolve each into x- and y-components, add them, then find magnitude by Pythagoras and direction by arctan.
Worked example
Forces (3, 4) and (1, −2) sum to (4, 2), magnitude √20 ≈ 4.47, direction ≈ 26.6°.
Real-world uses
- Calculating the net force on a boat pulled by two ropes or a crane load with angled cables
Common mistake
Adding magnitudes without considering direction.
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 Resultant Forces?
Add vectors using trigonometry. It is a topic at the advanced level in Trigonometry.
Where is Resultant Forces used in real life?
Real-world examples: Calculating the net force on a boat pulled by two ropes or a crane load with angled cables.
What should I learn before Resultant Forces?
Make sure you are comfortable with Vectors and Trigonometry, the previous topic in Trigonometry.
What is a common mistake with Resultant Forces?
Adding magnitudes without considering direction.
How can I practise Resultant Forces?
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 Resultant Forces?
Move on to Polar Coordinates 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.