By using the value of cosine function relations, we can easily find the value of sin 120 degrees. Using the trigonometry formula, sin (90 + a) = cos a, we can find the sin 120 value. We know that the value of cos 30 degrees is √3/2. Therefore, sin 120° = √3/2.

Important Angle Summary

1 Answer

• sin120=√32.
• cos120=−12.
• tan120=−√3.
• ctg120=−√33.
• sec120=−2.
• csec120=2√33.

#1: Memorize Common Angles and Coordinates

The value of Cos 120⁰ is – ½. It is the additive inverse of the value of cosine 60⁰ or cos 60⁰. Cosine is one of the basic trigonometric functions.

We know value of cosine of an angle in first and fourth quadrant is always positive. Think about 120° it is clear that 120° lies in second quadrant and -120° lies in fourth.

Answer: tan 120°= – √3.

Now after drawing a right-angled triangle POQ, we can calculate the value of Cos 30 degrees. Cos 30° =Length of the adjacent/length of the hypotenuse = OP/OQ.

The tangent of angle sixty degrees is a value that represents the ratio of lengths of opposite to adjacent sides when the angle of a right triangle equals to sixty degrees. The exact value for the tan of angle sixty degrees is square root of three.

From the above equations, we get sin 60 degrees exact value as √3/2.

30 Degrees

Sin 45° = /sqrt{2/4} = 1//sqrt{2}

Hence the value of Sin 75 degree is equal to (√3 + 1) / 2√2.

Answer: tan 75° = (√3 + 1) / (√3 – 1)