Trigonometry Basics: Sine Values

Trigonometric Ratios

• The table shows the values of trigonometric ratios for angles 0° to 90°:
  • sin A: 0 to 1
  • cos A: 1 to 0
  • tan A: 0 to not defined
  • cosec A: not defined to 1
  • sec A: 1 to not defined
  • cot A: not defined to 0

Using Trigonometric Ratios

• Example: In a right-angled triangle ABC, with AB = 5 cm and ∠ACB = 30°, find the lengths of BC and AC.
• To find the length of BC, use the trigonometric ratio involving BC and the given side AB.

Trigonometric Identities

• A trigonometric identity is an equation involving trigonometric ratios of an angle that is true for all values of the angle(s) involved.
• Example: In a right-angled triangle ABC, with AB^2 + BC^2 = AC^2, we can derive the identity:
  • cos^2 A + sin^2 A = 1
  • 1 + tan^2 A = sec^2 A

Finding Trigonometric Ratios

• If we know one trigonometric ratio, we can find the others.
• Example: If sin A = 1/3, then we can find the lengths of the sides of the triangle and hence the other trigonometric ratios.

Important Points

• The value of sin A or cos A is always less than 1 (or equal to 1) in a right triangle.
• The hypotenuse is the longest side in a right triangle.