Question

Using the unit circle, what is the calculated value of ?

Answer 1

I don’t see the trig expression you want evaluated — could you paste it?

Meanwhile, here’s a quick guide so you can evaluate any trig value from the unit circle:

- On the unit circle the point at angle θ (measured from the positive x-axis) is (cos θ, sin θ). So cos θ is the x-coordinate, sin θ the y-coordinate. Tan θ = sin θ / cos θ (when cos θ ≠ 0).

- Common angles (coordinates):
- 0 (0°): (1, 0)
- π/6 (30°): (√3/2, 1/2)
- π/4 (45°): (√2/2, √2/2)
- π/3 (60°): (1/2, √3/2)
- π/2 (90°): (0, 1)

- Use symmetry for other quadrants:
- Quadrant II (π/2 to π): x negative, y positive. Example: 5π/6 (150°) = (−√3/2, 1/2).
- Quadrant III (π to 3π/2): x and y negative.
- Quadrant IV (3π/2 to 2π): x positive, y negative.

- Reciprocals:
- sec θ = 1 / cos θ
- csc θ = 1 / sin θ
- cot θ = 1 / tan θ

If you send the specific angle/expression (for example cos(5π/6), sin(−π/4), tan(120°), etc.), I’ll compute its exact value for you.