Mr. Duval bought 21 calculators for his classroom. The total cost was
1 answer:
You might be interested in
Given:
The equation of a circle is
A tangent line l to the circle touches the circle at point P(1,3).
To find:
The equation of the line l.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is
Endpoints of the radius are O(0,0) and P(1,3). So, the slope of radius is
We know that the radius of a circle is always perpendicular to the tangent at the point of tangency.
Product of slopes of two perpendicular lines is always -1.
Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.
The slope of line l is and it passs through the point P(1,3). So, the equation of line l is
Adding 3 on both sides, we get
Therefore, the equation of line l is .
The unit circle is represented below:
As can be observed in the figure above, for an angle (t), the relation between the trigonometric functions and x and y components is:
x = cos(t)
y = sen(t)
x is positive in the first and in the fourth quadrant. Thus, cos (t) will be positive for angles in the first and fourth quadrant.
y is positive in the first and in the second quadrant. Thus, sin (t) will be positive for angles in the first and second quadrant.
