Answer :
- The reference angle of x = 7π/6
- sin (7π/6) = -1/2; tan (7π/6) = 1/√3; sec (7π/6) = -2/√3.
Define the term reference angle?
- The acute angle formed by the terminal arm or side as well as the x-axis is known as the reference angle.
- There is always a positive reference angle.
- The reference angle is, in other words, the angle formed by the terminal side as well as the x-axis.
Part A: The stated values is; x = 31π/6
A circle has 360 degrees. We must decrease the present angle to an angle between 0° and 360° in order to determine the reference angle.
As, 360° = 2π radians, subtract 2π = 12π/6 radians for each iteration.
Iteration 1 => 31π/6 - 12π/6 = 19π/6
Iteration 2 => 19π/6 - 12π/6 = 7π/6
0 ≤ 7π/6 ≤ 12π/6
Thus, reference angle is found as 7π/6 radians
Part B) The value for the sin x, tan x, and sec x.
sin (7π/6) = -1/2
tan (7π/6) = 1/√3
sec (7π/6) = 1/cos(7π/6) = -1/(√3)/2
sec (7π/6) = -2/√3
Thus, the simplest values of sin x, tan x, and sec x are found.
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