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!