KUMON METRO MANILA CENTER LEVEL M GUIDEBOOK In Level M, students begin by studying the basics of trigonometric functions, graphs and inequalities. Then they are introduced to more advanced trigonometric topics, including the Addition Theorem. At the end of Level M, students study analytic geometry.
FORMULAS TO HELP YOU IN TRIGONOMETRY The main trick to using formulas is to know what the different letters represent. In the formulas given here, you have: r (radius); d (diameter or distance); b (base or measure of a side); h(height); a, b, c (measures of sides); x, y (coordinates on a graph); m (slope);M (midpoint); h, k (horizontal and vertical distances from the center); θ (angle theta); and s (arc length). The formulas particular to trigonometry have: sin (sine), cos (cosine), and tan (tangent), although only sin is represented here.
KUMON METRO MANILA CENTER LEVEL M GUIDEBOOK
Right Triangle Definitions for Trigonometry Functions The basic trig functions can be defined with ratios created by dividing the lengths of the sides of a right triangle in a specific order. The label hypotenusealways remains the same — it’s the longest side. But the designations ofopposite and adjacent can change — depending on which angle you’re referring to at the time. The opposite side is always that side that doesn’t help make up the angle, and the adjacent side is always one of the sides of the angle.
KUMON METRO MANILA CENTER LEVEL M GUIDEBOOK
Coordinate Definitions for Trigonometry Functions The trig functions can be defined using the measures of the sides of a right triangle. But they also have very useful definitions using the coordinates of points on a graph. First, let let the vertex of an angle be at the origin — the point (0,0) — and let the initial side of that angle lie along the positive x-axis and the terminal side be a rotation in a counterclockwise motion. Then, when the point (x,y) lies on a circle that’s intersected by that terminal side, the trig functions are defined with the following ratios, where r is the radius of the circle.
Signs of Trigonometry Functions in Quadrants An angle is in standard position when its vertex is at the origin, its initial side is on the positive x-axis, and the terminal side rotates counterclockwise from the initial side. The position of the terminal side determines the sign of the various trig functions of that angle. The following shows you which functions are positive — and you can assume that the other functions are negative in that quadrant.
KUMON METRO MANILA CENTER LEVEL M GUIDEBOOK
Degree/Radian Equivalences for Selected Angles As you study trigonometry, you'll find occasions when you need to change degrees to radians, or vice versa. A formula for changing from degrees to radians or radians to degrees is:
The formula works for any angle, but the most commonly used angles and their equivalences are shown below.
