Find (if possible) the trig function of the quadrant angle.
sec 3pi/2
At 3π/2, a rotating arm ends up on the negative y-axis (270°)
If we consider a unit circle, then the terminal arm ends up at (0,-1), that is,
x=0, y = -1, r = 1
cos (3π/2) = 0/1 = 0
so sec(3π/2) = 1/cos(3π/2) = 1/0
which would be undefined.
IM the real master chief
To find the trigonometric function of an angle, we need to determine the reference angle. In this case, the given angle is 3π/2, which falls in the third quadrant of the unit circle.
In the third quadrant, the reference angle is the angle between the terminal side of the angle and the nearest x-axis. The reference angle for an angle in the third quadrant is equal to the angle in the first quadrant formed by the terminal side's projection onto the x-axis.
Since the angle 3π/2 falls in the third quadrant, the reference angle can be found by subtracting 2π from the given angle:
reference angle = 3π/2 - 2π = 3π/2 - 4π/2 = -π/2
Now, we need to determine the trigonometric function of the reference angle, which is in the fourth quadrant. In the fourth quadrant, the cosine function is positive (cosθ > 0), while the other functions (sine, tangent, cosecant, secant, and cotangent) are negative.
Since we're looking for the secant function of the angle, we know that secθ is equal to 1/cosθ. In the fourth quadrant, the cosine function is positive, so we can find the cosine of the reference angle (θ) and then calculate the secant:
cos(-π/2) = 0
Since the cosine of -π/2 is 0, the secant of -π/2 is undefined because division by zero is not possible.
Therefore, the secant function of the angle 3π/2 (in the third quadrant) is undefined.