Use the Reference Angle Theorem to find the exact value of sec(13 pi/6).
sec(13pi/6) = sec((13p1/6)*180/pi) =
sec(390 deg) = sec(390 - 360) = 30 deg,
sec(30 deg) = 2(sqrt3) / 3.
To find the exact value of sec(13pi/6) using the Reference Angle Theorem, we need to first determine the reference angle.
The Reference Angle Theorem states that for any angle in a standard position (angle whose initial side lies along the positive x-axis) with measure θ, the reference angle is the acute angle formed between the terminal side of θ and the x-axis.
In this case, our angle is 13pi/6. To determine the reference angle, we need to bring our angle to a standard position.
Step 1: Convert the angle to a multiple of pi/6
13pi/6 = 2pi/6 + pi/6 = (2 + 1)pi/6 = 3pi/6 = pi/2
Step 2: Determine the reference angle
To get the reference angle, we subtract the converted angle from pi/2:
Reference angle = pi/2 - pi/2 = 0
Now that we have determined the reference angle, we can proceed to find the value of sec(13pi/6).
The secant function is the reciprocal of the cosine function. Therefore, to find sec(13pi/6) we need to find the cosine of the reference angle and then take its reciprocal.
Step 3: Find the cosine of the reference angle
cos(0) = 1
Step 4: Take the reciprocal to find sec(13pi/6)
sec(13pi/6) = 1/cos(0) = 1/1 = 1
Therefore, the exact value of sec(13pi/6) is 1.