Trigonometry- Sin, Cos and Tan

Trigonometry- Sin, Cos and Tan

  • Trigonometry is concerned with the relationships between the sides and angles of triangles. The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan).

  • Sine (sin) of an angle in a right-angled triangle is the length of the opposite side divided by the length of the hypotenuse.

  • Cosine (cos) of an angle in a right-angled triangle is the length of the adjacent side (the side next to the angle) divided by the length of the hypotenuse.

  • Tangent (tan) of an angle in a right-angled triangle is the length of the opposite side divided by the length of the adjacent side.

  • Remember SOHCAHTOA, a mnemonic which helps to recall these relationships:
    • SOH stands for Sine= Opposite/Hypotenuse
    • CAH stands for Cosine = Adjacent/Hypotenuse
    • TOA stands for Tangent = Opposite/Adjacent

  • Trigonometric functions can be used to find the angles of a right-angled triangle if the lengths of the sides are known. This is known as inverse trigonometry.

  • The inverse functions are Sin^-1, Cos^-1 and Tan^-1. If you know the ratio of the sides (opposite/hypotenuse, adjacent/hypotenuse, opposite/adjacent), you can use these inverse functions to find an angle.

  • The trigonometric ratios (sin, cos, and tan) can also be found for any angle using a scientific calculator, this is particularly useful for non-right angled triangles.

  • Be familiar with the unit circle and how it applies to trigonometry. It provides a geometric interpretation for those trigonometric functions and extends them to all real numbers.

  • The values of sin, cos, and tan repeat every 180 degrees or π radians. This is called periodicity.

  • Mastery over the trigonometric identities is also crucial. These include cos^2 θ + sin^2 θ = 1, sin(-θ) = -sinθ, cos(-θ) = cosθ, and tan(-θ) = -tanθ.

  • The trigonometric functions are fundamental in the study of periodic phenomena - like light and sound waves - and in the calculation of distances and angles in fields like astronomy, cartography, and navigation. Thus, it’s not just about trigonometry within the context of mathematics, but an understanding of its practical application in various fields.