Trigonometric Ratios for Specific Angles
Understanding the values of trigonometric ratios for key angles is essential in trigonometry. Below are the values for the angles 120°, 135°, 150°, 180°, and 270° for all six trigonometric ratios.
1. Angle: 120°
- Sine (sin):
√3/2 - Cosine (cos):
-1/2 - Tangent (tan):
-√3 - Cosecant (csc):
2/√3 - Secant (sec):
-2 - Cotangent (cot):
-1/√3
2. Angle: 135°
- Sine (sin):
√2/2 - Cosine (cos):
-√2/2 - Tangent (tan):
-1 - Cosecant (csc):
√2 - Secant (sec):
-√2 - Cotangent (cot):
-1
3. Angle: 150°
- Sine (sin):
1/2 - Cosine (cos):
-√3/2 - Tangent (tan):
-1/√3 - Cosecant (csc):
2 - Secant (sec):
-2/√3 - Cotangent (cot):
-√3
4. Angle: 180°
- Sine (sin):
0 - Cosine (cos):
-1 - Tangent (tan):
0 - Cosecant (csc):
undefined(as sin = 0) - Secant (sec):
-1 - Cotangent (cot):
undefined(as tan = 0)
5. Angle: 270°
- Sine (sin):
-1 - Cosine (cos):
0 - Tangent (tan):
undefined(as cos = 0) - Cosecant (csc):
-1 - Secant (sec):
undefined(as cos = 0) - Cotangent (cot):
0
These values are crucial for solving various trigonometric problems and for understanding the behavior of trigonometric functions across different angles.