Find two values for theta such that theta is greater than or equal to 0 but less than or equal to 2pi.
1. Tan theta=1.1071
2. Sin theta = -0.8818
tan .836 = 1.1071
tanθ > 0 in QI, QIII
So, θ = 1.1071 or 1.1071+π
sin 1.080 = 0.8818
sinθ < 0 in QIII and QIV
So, θ = π+0.8818 or 2π-0.8818
To find two values for theta that satisfy the given conditions, we can use trigonometric identities and the unit circle.
1. Tan(theta) = 1.1071:
First, we need to find the principal angle that has a tangent of 1.1071. We can use the inverse tangent function (arctan) to find the principal angle.
arctan(1.1071) ≈ 0.902
Since we are looking for values of theta between 0 and 2pi, we can add 2pi to the principal angle to find the second value.
0.902 + 2pi ≈ 0.902 + 6.283 ≈ 7.185
Therefore, one value for theta is approximately 0.902 radians, and the other value is approximately 7.185 radians.
2. Sin(theta) = -0.8818:
Similar to the previous example, we can find the principal angle using the inverse sine function (arcsin).
arcsin(-0.8818) ≈ -1.095
Again, we can add 2pi to the principal angle to find the second value.
-1.095 + 2pi ≈ -1.095 + 6.283 ≈ 5.188
Therefore, one value for theta is approximately -1.095 radians, and the other value is approximately 5.188 radians.
Note: The given conditions of theta being greater than or equal to 0 but less than or equal to 2pi indicate that you are looking for angles within one complete revolution or between 0 and 360 degrees. Keep in mind that the angles provided are in radians.