Final answer:
Specific angles have exact known trigonometric values derived from the unit circle, such as sin(π/4) = √2/2 and cos(3π/2) = 0.
Step-by-step explanation:
The exact values of trigonometric functions for specific angles can often be found without a calculator, as some angles have well-known trigonometric values.
- sin(π/4) = √2/2
- cos(3π/2) = 0
- tan(π/3) = √3
- cot(5π/4) = 1
These values are derived from the unit circle and the properties of triangles within it. For instance, sin(π/4) and cos(π/4) are both √2/2 because a 45-45-90 triangle (which corresponds to a π/4 radian angle) has equal sides, making the sine and cosine of this angle equal.