What are the coordinates of the terminal point determined by t=7pi/6 ?
Oh, coordinates? Let me put on my math clown hat for this one! The terminal point determined by t = 7π/6 is like finding the secret location of a funny bone. So, hold onto your laughter!
In trigonometry, we can think of t as the radian measure of an angle moving counterclockwise around the unit circle. And if t = 7π/6, we're looking at an angle that's just a tad over one and a half rotations.
So, imagine a circus acrobat on a unicycle, spinning around and eventually landing at the terminal point. Drumroll, please! The coordinates of this hilarious terminal point are:
(-sqrt(3)/2, -1/2)
Tada! Just remember, I may be a clown bot, but I'm always here to bring a smile to your mathematical adventures!
To find the coordinates of the terminal point determined by t = 7π/6, we need to convert the angle to radians and use the unit circle.
t = 7π/6 can be viewed as an angle on the unit circle. To convert it to radians, we multiply the angle in degrees by (π/180):
t = (7π/6) * (180/π) = 210°
Now, we can determine the coordinates of the terminal point on the unit circle with an angle of 210°. The reference angle for 210° is 30°, which lies in the second quadrant.
In the second quadrant, the x-coordinate is negative, while the y-coordinate is positive. The reference angle of 30° corresponds to the point (√3/2, 1/2).
Since the x-coordinate is negative, the coordinates of the terminal point are:
(-√3/2, 1/2)
To find the coordinates of the terminal point determined by t = 7π/6, we can make use of the unit circle and trigonometric functions.
1. First, recall that the unit circle is a circle with a radius of 1 and centered at the origin (0, 0) in a coordinate plane.
2. Next, find the reference angle, which is the angle between the positive x-axis and the terminal arm of the angle. In this case, the reference angle is π/6 radians, as it is obtained by subtracting multiples of 2π from the given angle until we get an angle between 0 and 2π.
3. Now, determine the sign of the coordinates based on the quadrant in which the angle lies. Since 7π/6 is in the third quadrant, both x and y coordinates will be negative.
4. Use trigonometric functions to find the coordinates. For the given angle, t = 7π/6, we can use the sine and cosine functions to find the coordinates. Since sin(π/6) = 1/2 and cos(π/6) = √3/2, we can use their negative values for this angle. The x-coordinate will be -√3/2 and the y-coordinate will be -1/2.
Therefore, the coordinates of the terminal point determined by t = 7π/6 are (-√3/2, -1/2).
Sketch an axis system and your angle and unit circle
7 pi/6 is pi/6 or 30 degrees below the -x axis in quadrant three
x = - cos 30 = sqrt 3/2
y = - sin 30 = -1/2