How much trigonometry should one know for Subtest I?
Trigonometry makes an appearance in Subtest I in the context of Vectors. A vector is an entity with magnitude (size) and direction, which is measured by the angle that the vector makes with the positive x-axis. For this, elementary trigonometry is routinely involved.
The trigonometry prerequisites for Vectors for the CSET Subtest I is minimal. You must know:
* how to convert radian measure to degrees and vice versa: Angles are often represented in radians rather than degrees in Algebra II and beyond, and the conversion is
pi [yes, the symbol!] radians ~ 180 degrees.
So, simply use proportions to convert radians into degrees and vice versa.
* how to evaluate basic trigonometric functions for different degrees/radians using the notion of REFERENCE ANGLE (which is the smallest angle the ray makes with the x-axis).
--------------------------------------------------------------
Quick links: Current List of Articles in ARCHIVES, TESTIMONIALS & FEEDBACK and CONTACT ME!
--------------------------------------------------------------
You must also know the sin, cos and tan of 0, 30, 45, 60 and 90 degrees. Here's a nifty trick to construct a table of sin, cos and tan of 0, 30, 45, 60 and 90 degrees IN UNDER 1 MINUTE!!!
1. Make a table with 0, 30, 45, 60 and 90 degrees ON TOP in a "row".
2. Write sin, cos and tan to the left - in a "column" - one beneath the other.
3. Fill in the sin "row" - underneath 0, 30, 45, 60 and 90 degrees respectively - with 0, 1, 2, 3 and 4.
4. Next, divide EACH # [0, 1, 2, 3 and 4] by 4: 0/4, 1/4, 2/4, 3/4 and 4/4.
5. Finally, take Square Roots and simplify:
0, 1/2, r(2)/2, r(3)/2 and 1 which are the values for sin of 0, 30, 45, 60 and 90 degrees, respectively!
--------------------------------------------------------------
Quick links: Current List of Articles in ARCHIVES, TESTIMONIALS & FEEDBACK and CONTACT ME!
--------------------------------------------------------------
6. For cos: write the sin-row BACKWARDS! [since cos(x) = sin (90-x)...]
7. For tan x = sin x/cos x, simply find the ratio (mentally!) of the sin and cos of the angle desired!
[Tip: the denominators ALWAYS cancel out...so simply take the ratio of NUMERATORS alone! Try it to see what I'm blathering about...]
* the definitions ONLY of the 6 (or 3 MAIN) trigonometric ratios - sin, cos and tan of an angle - and the BASIC Pythagorean Identity: sin-squared A + cos-squared A = 1
Re INVERSE TRIGONOMETRIC functions ie. working backwards, for instance tan x = -1 in the 2nd quadrant, so x = ?, here's how to work them:
You see, if you can construct the sin-cos-tan "table of values" in ~ a minute, you just need to a) find the reference angle, and b) consult the table and work backwards! [Of course, this assumes CORRECTLY that you are NOT going to encounter messy angles like 20 or 145 or 219 degrees! They shall ALL be "reducible" to 0-30-45-60-90 degrees...]
--------------------------------------------------------------
Quick links: Current List of Articles in ARCHIVES, TESTIMONIALS & FEEDBACK and CONTACT ME!
--------------------------------------------------------------
For instance if cos Angle = - r(3) / 2 where r ~ ROOT, and you KNOW that the vector - from the given sketch or some other given info - is in, say, the 2nd quadrant, then, consulting the Trigonometric Table of Values you constructed, COS (30) = r(3)/2 => the Angle makes a 30 degree angle with the x-axis in the 2nd quadrant => Required Angle = 180 - 30 = 150 degrees. VOILA!
Likewise, if TAN Angle = r(3) where r ~ ROOT, and you KNOW that the vector - from the given sketch or some other given info - is in, say, the 3rd quadrant, then, consulting the Trig. Table of Values, TAN (60) = r(3) => Angle makes a 60 degree angle with the x-axis in the 3rd quadrant => Required Angle = 180 + 60 = 240 degrees. VOILA!
Hankering for more CSET Math Qs? Click on Need More Practice Questions? To purchase a vast database of Qs that I've compiled from my experience as a test taker and CSET Single Subject Math instructor at Cal State, San Bernardino, email me at innovationguy@yahoo.com. The CSET Qs on this site are taken from that collection of questions!
If you found this site useful, be an evangelist and please spread the word to other CSET Single Subject Math examinees, and support this site with a contribution via Paypal!
Posts
No comments:
Post a Comment