Having looked at trigonometric ratios in quadrants, we now look at examples of calculating trigonometric values in quadrants.

**Example 1**: sin 30° = 0.5

**Example 2**: sin 100° = sin (180 – 80)

= sin 80°

= 0.9848

Since 100° is in the second quadrant, the sine value is positive

**Example 3**: cos 120° = cos (180 – 60)

= -cos(60°) = -0.5

using cos (180 – θ) = -cos θ

Cosine value in second quadrant is negative, as 120° is in second quadrant

**Example 4**: tan 60° = 1.732. What is tan 120°?

tan 120° = tan (180 – 60)

= -tan (60°) = -1.732

120° is in second quadrant, and tangent value in second quadrant is negative.

**Example 5**: sin 200° = sin (180 + 20)

This angle is in the third quadrant, and sine value is negative in this quadrant

sin (180 + θ) = -sin θ

So sin 200 = sin (180 + 20) = -sin 20°

= -0.342

**Example 6**: cos 300° = cos (360 – 60)

300° is in the fourth quadrant, and cosine value is positive in this quadrant

cos (360 – θ) = cos θ

So cos 300° = cos (360 – 60)

= cos 60°

= 0.5

**Example 7**: tan (-50°) = tan (360 – 50)

-50° is in the fourth quadrant, and tangent value is negative in this quadrant

tan (360 – θ) = -tan θ = tan (-θ)

So tan (-50) = -tan 50°

= -1.1918

**Example 8**: tan (-110°) = ?

Angle -110° = 360 – 110 = 250° which is in the third quadrant. So tangent value is positive in third quadrant.

Hence tan (-110°) = -tan (110°) = -tan (180° – 70°)

= −(−tan 70°) = tan (70°)

= 2.7475

## Trigonometric Values without Calculator

Without using the calculator, let us try to answer whether these trigonometric values are positive or negative.

**1. cos 280° = ?**

280° lies in the fourth quadrant, so cosine is positive

**2. sin 300° = ?**

300° lies in the fourth quadrant, and sine is negative

**3. tan 240° = ?**

240° lies in the third quadrant, and tan is positive

**4. sin 210° = ?**

210° lies in the third quadrant, and sine is negative

**5. cos 170° = ?**

170° lies in the second quadrant, and cosine is negative