1. Guide to Evaluating and converting A math methods presentation by Aleesha Davis
2. 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° = πc 180
4. convert Example Convert 30° to radians Solution Since 1° = πc 180 30° = 30 × πc 180 = πc 6
5. 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
6. 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)
7. 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.
8. Evaluate Example 1 Evaluate sin π and cos π Solution In moving through an angle of π, the position P(π), which is (-1,0). Therefore, cos π = -1 and sin π = 0
9. 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.
10. Evaluate Example Evaluate cos Solution cos = cos(π + ) =–cos (by symmetry) = Note– Symmetry properties can be found on page 199
11. Evaluate Questions to complete Exercise 6B – Questions 2 all, 3 all, 4* Exercise 6C – Questions 1* and 3* Exercise 6E – Questions 1 and 2
