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.

Infinite sums, getting towards the idea of integration

Worked on problems related to the early ideas of calculus today.

The ideas today were closer to integration, finding an area using a summation of infinitely small rectangles using limits.

That meant finding the area of one rectangle and adding up all of them. So a base multiplied by a width.

The actual shape was a triangle and rectangle, but the technique becomes more useful for shapes which are not easy to calculate.

There were quite a few steps, so a single mistake could throw everything off.

Algebra at CSUMB with trig identities- sine, cosine, tangent, cosecant, secant, cotangent

We mostly did problems with trig identities.

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Reduced a few radicals to a simpler form.

Talked about how the 30 60 90 triangle and 45 45 90 triangles have ratios that you should probably know in this context.

Algebra at CSUMB with logarithms

We mostly looked at problems with logarithms.

Used both the properties for the log of a product and the log of a quotient.

Saw how the base, exponent, and result are placed in the equations.

Graphed a few related functions. You can graph functions using an x and y grid and using points. It helps to know the shape in advance, but that’s not completely necessary.

RLS Friday sheet Precalculus tutoring – fourth order polynomial with complex numbers

We started by talking about the Lorentz Force Law which makes many problems with forces and magnetism make more sense in my opinion.

Then looked at a Friday sheet.

Did a problem with complex numbers starting with a fourth order polynomial  that had two zeros given. It involved either long division or synthetic division, we used long division.

Another problem had logarithms. e^x and lnx are functions that counteract each other.

The half angle formula was used for another problem.

Starting to look at limits in precalculus

We looked at limits in the context of the last few weeks of precalculus.

All of the functions we saw had a (single) removable discontinuity or hole. The limits were found for that point and two other points. For the limit to exist, it needs to go to the same place from the right and from the left.

It didn’t exactly make sense to find a limit for points that did not have holes, but that was part of some of the problems.

Tutoring Conceptual Physics at RLS

We looked at conceptual problems related to magnetism. The book used by the school doesn’t use equations much. Which seems like a strange approach to me.

I think it would be useful to see something like the Lorentz Force Law which involves the movement of a point charge in a magnetic field and has a cross product.

F=qvxB, where F, v, and B are vectors. The right hand rule can be used with the cross product.

Can look more at this later on, will bring another book.

Tutoring math at CSUMB, systems of equations and quadratic equations

We started by looking at systems of two equations with two variables and using substitution to solve.

Then did a few problems with three equations and three variables.

Also used u-substitution to solve a few quadratic equations. If they can be factored, that can be easier. Sometimes quadratic equations cannot be easily factored, in which case it can be useful to use the Quadratic Formula.