To find the exact values of the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent) for an angle of 8 degrees, we can use the definitions of these ratios in relation to a right triangle.
First, we recall the definitions:
- Sine (sin): Ratio of the length of the opposite side to the hypotenuse.
- Cosine (cos): Ratio of the length of the adjacent side to the hypotenuse.
- Tangent (tan): Ratio of the length of the opposite side to the adjacent side.
- Cosecant (csc): Reciprocal of sine. (csc = 1/sin)
- Secant (sec): Reciprocal of cosine. (sec = 1/cos)
- Cotangent (cot): Reciprocal of tangent. (cot = 1/tan)
For an angle of 8 degrees, we can either use a scientific calculator or trigonometric tables to find these values:
- sin(8°) ≈ 0.1392
- cos(8°) ≈ 0.9903
- tan(8°) ≈ 0.1395
- csc(8°) ≈ 7.198
- sec(8°) ≈ 1.0104
- cot(8°) ≈ 7.151
In summary, the six trigonometric ratios for an angle of 8 degrees are approximately:
- sin(8°) = 0.1392
- cos(8°) = 0.9903
- tan(8°) = 0.1395
- csc(8°) = 7.198
- sec(8°) = 1.0104
- cot(8°) = 7.151
These values can be helpful in various applications of trigonometry, especially when working with angles and triangles.