Precalculus with Interval Notation in My Math Lab – square/curved

We first looked at plotting a function. It helps to recognize the shape of the graph from the equation, but if you don’t, you still move to the next steps you would even if you know the general shape- you plot specific points.

A good point to start with most of the time is the y-intercept, you get that by setting x equal to zero.

From there, plot a few points. If you know there is symmetry, that can make the calculations easier.

Then we looked at linear equations for a while. We saw how the slope is written before the variable (oftentimes x) and that the y-intercept is the number after that (in slope intercept form).

Found the slope using the equation. And also saw that ‘average rate of change’ is the slope.

Went over interval notation a bit. In ‘My Math Lab’, [ are inclusive and ( are exclusive. You use the exclusive brackets for infinity since it’s not a specific point.

Tutoring Precalculus at MPC

We started by looking at how to factor trinomials. One option is to write two sets of parentheses. From there I look first at the first term, then at the third term. And I use the middle term to guide my choices.

There is another method that uses similar ideas but that is laid out in four sections of a large X.

Talked about when the quadratic formula is useful and used it a few times.

Got into algebraic perfect squares.

Did a bit with inequalities.

Saw some complex numbers.

Used the Pythagorean Theorem once.

Looked at a parabola, intercepts, and symmetry.

Three log rules – power, product, quotient

I tend to use the natural log (ln).

Reviewing for RLS AATP Final

We did problems with trigonometry reviewing for the final.

The six trig functions are the ones in the two acronyms
SOHCAHTOA
CHOSHACAO

Sine, cosine, tangent, cosecant, secant, cotangent

One problem had numbers that looked like a 30 60 90 triangle.

A few times, the substitution of 1 = sin^2x + cos^2x

The trig functions can all be written in terms of sine and cosine and really, you could even write everything in terms of sine (but that wouldn’t be useful in this context).

It would help sometimes to be more comfortable with radians.

Why you should not use the Law of Sines if you can use SOHCAHTOA instead

We went over some of the harder problems from previous tests. Some dealt with the Law of Sines and the Law of Cosines.

Others could simply use SOHCAHTOA. If you have a right triangle and one angle and a side (you could get the other angle beside the right angle easily) then you can use SOHCAHTOA.

That will be simpler and less steps and will reduce to the same thing as using the Law of Sines.

How to use logarithms to solve a problem with a variable exponent

Reviewing for RLS Final, Trig Functions

We reviewed for the final by mostly going over problems with trig functions.

SOHCAHTOA
CHOSHACAO

Understanding the reciprocal relationships was useful for a few problems.

Sometimes the double angle and half angle formulas were used.

Rewriting the functions in terms of sinx and cosx can be useful. As is knowing that sin^2x + cos^2x = 1 .

It would be helpful to memorize that
sin(0°) = 0
sin(90°) = 1
cos(0°) = 1
cos(90°) = 0

Graphing Trig Functions

We worked mostly on problems with trigonometric functions.

A few involved graphing the functions. It can help quite a bit to know the shape of the graph in advance. But, if you do not, or even if you somewhat do, then you can use

SOHCAHTOA
CHOSHACAO

Also used some double angle formulas and saw how you can use the trig functions with sums for double angle formulas.

Logarithm Properties, Tutoring at RLS

We worked on a problem with exponents and algebra.

Logarithms can be very useful for these problems.

There are three basic properties which are often used, two of them were used in this problem.

The logarithm of a quotient is the logarithm of the numerator minus the logarithm of the denominator.

The logarithm of a product is the logarithm of the first term plus the logarithm of the second term.

And the logarithm of something with an exponent brings the exponent in front of the expression as a multiplication.

Tutoring Law of Cosines, RLS Friday Sheet

We mostly worked on problems with the Law of Cosines. Along with the Law of Sines, this equation can be helpful in figuring out sides and angles of triangles. The Law of Cosines is the Pythagorean Theorem generalized for triangles that are not right triangles.

Also looked at a Friday sheet. One problem with exponents and logarithms was the most involved.

Another involved asymptotes.