To find the sine, cosine, and tangent of 5π/4 radians, we can start by recognizing that this angle is located in the third quadrant of the unit circle.
The angle 5π/4 radians is equivalent to 225 degrees. In the third quadrant, both sine and cosine values are negative, while the tangent value is positive.
Now, using the reference angle of π/4 radians (or 45 degrees), we can determine the values:
- Sine (sin): The sine of 5π/4 is -√2/2.
- Cosine (cos): The cosine of 5π/4 is -√2/2.
- Tangent (tan): The tangent of 5π/4 is 1 (since it is the ratio of sine to cosine: -√2/2 ÷ -√2/2 = 1).
In summary:
- sin(5π/4) = -√2/2
- cos(5π/4) = -√2/2
- tan(5π/4) = 1