BeginnerTopic 13 of 104Engineering Mathematics
Trigonometry basics
Sine, cosine and tangent relate angles to side ratios in right triangles.
In depth
In a right triangle sin=opposite/hypotenuse, cos=adjacent/hypotenuse and tan=opposite/adjacent (SOH-CAH-TOA). The ratios depend only on the angle. They resolve forces into components and determine heights and distances in surveying.
Key points
- Pythagoras: a²+b²=c²
- Special angles: 30°, 45°, 60°
- Inverse functions find angles
ExampleA 100 N force at 30° has a horizontal component 100cos30° ≈ 86.6 N.
Right-triangle trigonometry links angles to lengths, forces and heights, and it is the start of every wave and rotation calculation.
What is Trigonometry basics?
Sine, cosine and tangent relate angles to side ratios in right triangles.
Why is it important to understand trigonometry basics?
Right-triangle trigonometry links angles to lengths, forces and heights, and it is the start of every wave and rotation calculation.
When should I use sine versus cosine?
Use sine for the opposite side over the hypotenuse and cosine for the adjacent side. Drawing the triangle with the known angle clearly marked avoids mistakes.
Why do calculators sometimes give the wrong angle?
Many calculators are set to degrees or radians by default. Always check the angle mode before using inverse functions.
How is Trigonometry basics used in practice?
Typical applications include resolving a cable tension into horizontal and vertical components, measuring the height of a tower from a known distance and finding the phase angle between two signals.
What should I learn before Trigonometry basics?
Study "Functions and graphs" first (topic 12 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Trigonometry basics?
Pythagoras: a²+b²=c². Special angles: 30°, 45°, 60°. Inverse functions find angles.
Can you give an example of Trigonometry basics?
A 100 N force at 30° has a horizontal component 100cos30° ≈ 86.6 N.
What comes after Trigonometry basics?
The next topic is "Radians and angular measure", which builds directly on this one.
How difficult is Trigonometry basics?
It is classed as Beginner in Engineering Mathematics (topic 13 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.