Wednesday, November 08, 2023

Essential Trigonometry

Trigonometry is one of the most important and widely applied branches of mathematics. It comes in two flavors: triangle trigonometry and circular trigonometry. 

Triangle trigonometry, the kind featured on the SAT/ACT, is concerned only with solving right triangles (i.e. finding unknown side lengths and angle measures).

A tiny number of basic trig facts and processes are tested in a relatively small number of SAT/ACT math questions. Nevertheless, students aiming for top scores must master each of these elements.

Following is what you need to know.

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Three primary trig ratios
Definition: SOH CAH TOA (sin, cos, tan).

Solving right triangles using SOH CAH TOA

Converting radians to/from degrees 
1rad = 180/pi.
1deg = pi/180.

Sinusoidal curves
Amplitude: vertical distance between midline and upper/lower bound.
Period: horizontal distance between repeating points on the curve (e.g. peaks).

Cofunctions of compliments are equal
For example: sin(50 degrees) = cos(40 degrees).

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For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this important material.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Wednesday, November 01, 2023

Look Inside the Digital SAT

The digital SAT has arrived, 

In the meantime, much has been written about all aspects of this latest incarnation of the SAT. All along, The College Board has offered limited information concerning what we who care should expect.

But the private analyses of those whose businesses and livelihoods hinge on gaining an early, accurate, and comprehensive view of this strange new beast are also well worth noting.

In addition to those featured on the SAT/dSAT resource page of my business site, below are several more such reports.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.