Understanding the Values of Sine, Cosine, and Tangent
To find the sine, cosine, and tangent values for the angle 8π/4 radians, we first simplify the angle:
- 8π/4 = 2π (since 8 divided by 4 equals 2).
The angle 2π radians corresponds to a full rotation (360 degrees) around the unit circle. Therefore, it lands on the same point as:
- 0 radians (or 0 degrees).
Now, let’s calculate the values:
- Sine (sin) of 2π (or 0): sin(2π) = 0
- Cosine (cos) of 2π (or 0): cos(2π) = 1
- Tangent (tan) of 2π (or 0): tan(2π) = 0 (since tan = sin/cos and sin(2π) = 0)
Final Values:
- Sine: 0
- Cosine: 1
- Tangent: 0
In conclusion, for the angle 8π/4 radians, the values are:
- sin(8π/4) = 0
- cos(8π/4) = 1
- tan(8π/4) = 0