Trigonometry- Common Values
Trigonometry- Common Values
Introduction to Trigonometry
- Trigonometry is the study of the relationships between the angles and sides of triangles.
- Trigonometry is especially useful in right-angled triangles, where the relationships between angles and sides are regular and predictable.
- The three main trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).
Sin, Cos, and Tan
- To calculate sin of an angle, divide the length of the opposite side by the length of the hypotenuse.
- To calculate cos of an angle, divide the length of the adjacent side by the length of the hypotenuse.
- To calculate tan of an angle, divide the length of the opposite side by the length of the adjacent side.
- The acronyms SOH, CAH, and TOA (standing for Sine = Opposite ÷ Hypotenuse, Cosine = Adjacent ÷ Hypotenuse, Tangent = Opposite ÷ Adjacent) can help to remember these formulas.
Common Values
- The trig ratios have common values for some angles that are worth memorising.
- These angles include the multiples of 30, 45 and 60 degrees.
- At 30°, sin = 0.5, cos = √3/2, and tan = √3/3.
- At 45°, sin = √2/2, cos = √2/2, and tan = 1.
- At 60°, sin = √3/2, cos = 0.5, and tan = √3.
- Remember, these common values are for angles in degrees, not radians.
Trigonometric Applications
- Trigonometry is used in many areas of mathematics and in real-world applications, including physics, engineering, and computer graphics.
- It’s also used for calculating distances and angles in geography and in many fields that work with measurements and maps.
- Trigonometric ratios are key to solving problems involving right-angled triangles and can also be used to check if a triangle is right-angled.
Practice and Understanding
- As with all areas of mathematics, practice is key to mastering trigonometry.
- Regularly review and use sin, cos, and tan in a variety of contexts.
- Try out practice questions with different angles and side lengths to understand how the ratios change.
- Trigonometry is not just about memorising formulas – it’s about understanding how angles and lengths are related.
- Deeper understanding will come with continued practice and application. So, keep practicing and exploring different problems!