The value of sin 120 degrees is

The value of sin 120 degrees is

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Question

The value of sin 120 degrees is

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