We started the day with a warmup using the
trig basics Quizlet. During the class, Mr. O'Brien wants to talk about patterns, tan π/6 vs. tan π/3, sec 5π/3, quadrants, reference angles, even/odd, periodicity, identities: reciprocal, quotient, pythagorean, co-function. We went back to the applets (found here:
sine box,
cosine box, and
unit circle).
We used the sine box to go over finding different values without a calculator. Mr. O'Brien reminded us the sine value is the y and the cosine value is the x. He also told us that the x values (cosine) are positive in Quadrant I and Quadrant IV, and that the y values (sine) are positive in Quadrant I and Quadrant II. He also told us that the tangent values are positive in Quadrant I and Quadrant III. Mr. O'Brien gave us a mnemonic to remind us which values are positive:
All
Students
Take
Calculus. This tells us that in Quadrant I, all values are positive. In Quadrant II, sine values are positive. In Quadrant III, tangent values are positive. And in Quadrant IV, cosine values are positive. Mr. O'Brien gave us a table to show patterns that help us remember some of the values:
After this we went over the difference between tan π/6 and tan π/3.
Then we moved on to the
all 198 trig values Quizlet and discussed identities. Andy showed the which trig functions are which, copied below:
We went over the reciprocals of trig functions.
You can find a table of the trigonometric identities here (it includes reciprocal, Pythagorean, quotient, and co-function identities, as well as others that we don't need). Note that it uses an upsi
lon (υ) instead of a theta (θ). We worked through a few values, such as the ones below:
Example: If we have a value like sec(135˚), we know that it's positive because of all students take calculus. We know that the reference angle is 45˚, and that it corresponds to cosine. So, we know that it's the reciprocal of cos(45˚) which is -√2.
Mr. O'Brien told us that if we want to use our calculator to evalute something such as secant, we have to enter it as cos(x)^-1. He told us that cos^-1(x) is
not the same as sec(x). He also told us that
and that you have to enter the latter in a calculator, as it won't allow you to enter the former.
In the last two minutes of class, we went over the homework problems. For #29, we just had to recognize that sin 5π=sin π. For #43, he reminded us that we had to change our calculator from degree to radian mode. To do this, simply hit the [MODE] button on the calculator, and select radian. Katherine brought up the point that if we have our calculators in degree mode, then we can simply enter sin π/4 into the calculator as sin (√2/2).
