have a look at what trig functions are
it is important to be able to evaluate most trig function values without a calculator
it’s a long journey ahead of us, and we’ll learn all this step by step…
common angles
how to evaluate trig functions for common angles
sign
sine and cosine have the range , and we can divide that into four quadrants, to make evaluating trig functions much easier
looking at the unit circle, this is a table showing the signs of the outputs of trig functions for the quadrants
| quadrant | sin | cos | tan |
|---|---|---|---|
| 1 | positive | positive | positive |
| 2 | positive | negative | negative |
| 3 | negative | negative | positive |
| 4 | negative | positive | negative |
we can make a shorter table that we need to remember. just remember the letters “ASTC”
| quadrant | what is positive |
|---|---|
| 1 | all |
| 2 | sin |
| 3 | tan |
| 4 | cos |
this is important, because this is the easiest way to find out the sign of an angle. no matter what angle you have, if you know which quadrant the angle is, you know the sign of the sine, cosine and tan outputs
symmetry properties
how to evaluate trig functions with symmetry properties
supplementary identities
how to evaluate trig functions with supplementary identities
complementary identities
how to evaluate trig functions with complementary identities
sum and difference identities
how to evaluate trig functions with sum and difference identities
double and half angle identities
how to evaluate trig functions with double and half angle identities