E-Lecture - Important Points
- If the two points (x1, y1) and (x2, y2) are two distinct points on a line with x2 - x1 ≠ 0, then the gradient (slope) of the line joining the two points is given by:
- The angle measured from positive x-axis to a line in counter clockwise direction is called the inclination of a line. The tangent of this angle is called the slope of the line. That is,
- Using the right triangle ABC which is a right angle at C and a, b, and c are the lengths of the sides opposite these angles, then the tangent, cosine and sine of an angle in relation to ∠A can be defined as follows:
- If we denote one of the two acute angles by θ, we can express the relation to the angle θ as follows:
- The point P (x, y) is the same as the point P(cos θ,sin θ)on the unit circle.
- The Law of Sine: If A, B, and C are the measures of the angles of a triangle ABC and a, b, and c are the lengths of the sides opposite these angles, then
- The Law of Cosine: If A, B, and C are the measures of the angles of a triangle ABC and a, b, and c are the lengths of the sides opposite these angles, then
c2 = a2 + b2 − 2ab cos C
b2 = a2 + c2 − 2ac cos B
a2 = b2 + c2 − 2bc cos A - The line which is drawn from the eyes of the observer to the point being viewed on the object is known as the line of sight.
- The angle of elevation of the point on the object (above the horizontal line) viewed by the observer is the angle which is formed by the line of sight with the horizontal line.
- The angle of depression of the point on the object (below the horizontal line) viewed by the observer is the angle which is formed by the line of sight with the horizontal line.
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