The value of sin 120 degrees is
The value of sin 120 degrees is

The value of sin 120 degrees is

Question

The value of sin 120 degrees is

Answer

sin 120 is one of the trigonometric ratios that is positive because it is in quadrant II. The value of sin 120° is equal to 3, to determine it, you can use the relation angle in quadrant II, namely (180° – ) or (90° + ).

 

Explanation

The quadrant in Cartesian coordinates consists of 4, namely

  • Quadrant I (0° – 90°) all trigonometry is positive. Relation angle used (90° – )
  • Quadrant II (90° – 180°) trigonometry with positive values is sine and cosecant. The relation angle (90° + ) or (180° – )
  • Quadrant III (180° – 270°) trigonometry with positive values is tangent and cotangent. The relation angle (180° + ) or (270° – )
  • Quadrant IV (270° – 360°) trigonometry with positive values is cosine and secant. The relation angle (270° + ) or (360° – ) or (- )

 

If using a 90° or 270° . relation angle

  • sin changes to cos (and vice versa)
  • sec changes to cosec (and vice versa)
  • tan turns into cot (and vice versa)

If using the relation angle 180° or 360° then

  • trigonometry is fixed

 

So the value of sin 120° is positive (because it is in quadrant II)

 

Using relation angles (90° + )

sin 120°

= sin(90° + 30°)

= cos 30°

3

 

Using relation angles (180° – )

sin 120°

= sin(180° – 60°)

= sin 60°

3

 

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Another example problem about sin 300°

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Class : 10

Course : Mathematics

Category : Trigonometry

Code : 10.2.7