Final answer:
To find the values of the trigonometric functions of t when cos(t) < 0 and (t) = 4, we need to determine the quadrant in which t lies and use the unit circle. The values of the trigonometric functions of t are: sin(t) ≈ 0.9949, cos(t) = -0.25, tan(t) ≈ -3.9796, cosec(t) = 1 / sin(t), sec(t) = 1 / cos(t), and cot(t) = 1 / tan(t).
Step-by-step explanation:
To find the values of the trigonometric functions of t when (t) = 4 and cos(t) < 0, we need to use the unit circle and quadrant rules. Since cos(t) < 0, we know that t lies in either the 2nd or 3rd quadrant. In the 2nd quadrant, sin(t) is positive, while in the 3rd quadrant, sin(t) is negative. Therefore, the values of the trigonometric functions of t are:
- sin(t) = √(1 - cos²(t)) = √(1 - (-0.25)²) = √(1 - 0.0625) ≈ 0.9949
- cos(t) = -0.25
- tan(t) = sin(t) / cos(t) ≈ 0.9949 / -0.25 ≈ -3.9796
- cosec(t) = 1 / sin(t)
- sec(t) = 1 / cos(t)
- cot(t) = 1 / tan(t)