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TRIGONOMETRYMath 12 Plane and Spherical Trigonometry

TRIGONOMETRYDerived from the Greek words trigonon which means triangle and metron which means to measure.

Branch of mathematics which deals with measurement of triangles (i.e., their sides and angles), or more specifically, with the indirect measurement of line segments and angles.

TRIANGLES

TRIANGLESClassification of triangles according to sides:Scalene Triangle - a triangle with no two sides equal.Isosceles Triangle - a triangle with two sides equal.Equilateral triangle a triangle with three sides equal.

CLASSIFICATION OF ANGLES

Lesson 1: ANGLE MEASUREMath 12 Plane and Spherical Trigonometry

Week 16

OBJECTIVESAt the end of the lesson the students are expected to:Measure angles in degrees and radiansDefine angles in standard positionConvert degree measure to radian measure and vice versaFind the measures of coterminal anglesCalculate the length of an arc along a circle.Solve problems involving arc length, angular velocity and linear velocity

ANGLEAn angle is formed by rotating a ray about its vertex from the initial side to the terminal side.An angle is said to be in standard position if its initial side is along the positive x-axis and its vertex is at the origin.Rotation in counterclockwise direction corresponds to a positive angle.Rotation in clockwise direction corresponds to a negative angle.

ANGLE MEASURE

CONVERTING BETWEEN DEGREES and RADIANS

COTERMINAL ANGLES

LENGTH OF A CIRCULAR ARC

LINEAR SPEED

ANGULAR SPEED

RELATIONSHIP BETWEEN LINEAR and ANGULAR SPEEDS

LINEAR and ANGULAR SPEED

Two pulleys, one 6 in. and the other 2 ft. in diameter, are connected by a belt. The larger pulley revolves at the rate of 60 rpm. Find the linear velocity in ft/min and calculate the angular velocity of the smaller pulley in rad/min.

The earth rotates about its axis once every 23 hrs 56 mins 4 secs, and the radius of the earth is 3960 mi. Find the linear speed of a point on the equator in mi/hr.

REFERENCESAlgebra and Trigonometry by Cynthia YoungTrigonometry by Jerome Hayden and Bettye Hall

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