GUIDE TO EVALUATING AND CONVERTINGA math methods presentation by Aleesha Davis

CONVERT

Definition - a change in the form of a quantity, a unit, or an expression without a change in the value 

The angle, in radians, swept out in one revolution of a circle is 2πc ( c is equal to radians)

2πc = 360°Therefore, πc = 180°

1c = 180° π

1° = π c

180

CONVERT

When converting from degrees to radians,

When converting from radians to degrees,

CONVERT

Example Convert 30° to radians

Solution

Since 1° = π c

180 30° = 30 × π c

180

= πc

6

CONVERT

Questions to complete Exercise 6A, Questions 1-4

Tips Make sure your calculator is in the correct

mode; radians or degrees depending on what question you are doing

EVALUATE

Definition -  To calculate the numerical value of; express numerically

 The unit circle is a circle of radius 1 unit.

P(θ) = (cos θ, sin θ)

EVALUATE Using symmetry

properties of the unit circle, we can determine how properties in each quadrant are written, and which of the trigonometric functions are positive. As displayed, in quadrant 1-all sin, cosine and tan are positive, in quadrant 2-only sin is positive, in quadrant 3-only tan is positive, and in quadrant 4-only cosine is positive.

EVALUATE

Example 1 Evaluate sin π and cos π

SolutionIn moving through an angle of π, the position

P(π), which is (-1,0).Therefore, cos π = -1and sin π = 0

EVALUATE

For the unit circle, the trigonometry ratios for the reference angles in the first quadrant are shown below. We use 30o-60o-90o and 45o-45o-90o triangles to determine these ratios.

angle sin cos tangentsincos

0o 0 1 0

30o 1/2 √3/3 √3/3

45o √2/2 √2/2 1

60o √3/2 1/2 √3

90o 1 0 undefined

EVALUATE

Example Evaluate cos

Solutioncos = cos(π + ) =–cos (by symmetry)

=

Note– Symmetry properties can be found on page 199

EVALUATE

Questions to complete Exercise 6B – Questions 2 all, 3 all, 4* Exercise 6C – Questions 1* and 3* Exercise 6E – Questions 1 and 2