The angle "a" on the unit circle, formed when the segment that connects the origin to point
P ( square root of 2 / -2; square root of 2 / -2) meets the positive x axis, can be written as 10P/a radians. What is the value of a?
do not understand
To find the value of angle "a", we can use the coordinates of point P and apply the concept of the unit circle.
Let's start by finding the coordinates of point P:
Given:
P(x, y) = (square root of 2 / -2, square root of 2 / -2)
Now, let's consider the unit circle:
The unit circle is a circle with a radius of 1, centered at the origin (0, 0). It is commonly used in trigonometry to relate the angles with their corresponding coordinates on the circle.
The positive x-axis intersects the unit circle at the point (1, 0).
Now, let's use the given point P and the unit circle to find the value of angle "a":
Since the x-coordinate of point P is negative (square root of 2 / -2), the angle "a" will be greater than 180 degrees. Let's find the angle "a" using the arctan function:
a = arctan(y/x)
= arctan((square root of 2 / -2) / (square root of 2 / -2))
= arctan(1)
= 45 degrees
Now, we need to convert the angle from degrees to radians. To convert degrees to radians, we can use the conversion factor:
1 radian = (pi/180) degrees
a (in radians) = 45 degrees × (pi/180 radians/degree)
= (45π)/180
= π/4 radians
Therefore, the value of angle "a" is π/4 radians.
Finally, to find the value of "a" in terms of the segment connecting the origin to point P, we multiply the angle by 10P:
a = 10P/a radians
= 10 × (π/4) radians
= 10π/4 radians
Simplifying further, we get:
a = 5π/2 radians
So, the value of "a" is 5π/2 radians.