Tutoring Trigonometry, Use Trig functions on right triangles!

We went over problems with trig functions.

The functions only work with right triangles.

Looked at both the angle of elevation and the angle of depression in a few problems.

The final two problems were more complicated and involved two equations and two unknowns as well as calculating the tangent function of two angles and factoring as well as multiplying algebraic expressions.

Graphing a hyperbola “neatly”, tutoring Algebra II

We started by graphing a hyperbola “neatly” as the directions stated. That involved finding the vertices, foci and drawing the diagonal asymptotes.

Checked one point by plugging in an x value to see if the graph was accurate.

The sign in front of the variables is important to determine orientation of the conic sections.

The natural number is e and is the base for the natural logarithm. e is approximately 2.7


We mostly looked at

Also finding the positions of angles and the names of equivalent angles.

Less than zero can be read as ‘negative’ and more than zero can be read as ‘positive’.

For these trig functions, the hypotenuse is always positive. And many times, using the unit circle is useful. Although, sometimes multiplying the ratios by a common factor can also be useful.

How do I solve 3^{2x}=81?

A few options. The option on the left assumes that the answer is a positive whole number.

The option on the left would be more useful for a not-whole number.


We started by looking at evaluating trig functions of angles. They involved 30 60 90 triangles and 45 45 90. So we began by looking at those triangles.

It’s easy enough to derive the ratios for the isosceles triangle.

Then we compared that to the other triangle.


Often, it helps to draw the angles on the xy axes starting from the 0° position (usually East). Then connect the angle to the x-axis to make a triangle.

Also, the functions are pronounced ‘sine’, ‘cosine’, ‘tangent’. If you’re going to say them out loud, say those, not “sin”, “cos”.

If you get to “csc”, how would you even say that out loud?

Algebra, Variables with Exponents Positive, Negative, and to the Zero

An explanation of why numbers to the zero power equal 1.

Dealing with exponents in various situations.

Finding X and Y Coordinates on a Graph

Slope Intercept Form and Finding the slope

Tutoring Algebra, slope and intercepts

We looked at slope intercept form and how m is the slope and b is the y- intercept.

To get the y-intercept, you set x = 0
to get the x-intercept, you set y = 0

To get the slope, you use two points (some are easier to work with than others)
x1, y1
x2, y2

Then take (y2 – y1)/(x2 – x1)

Subtracting a negative two is like like adding two

x – – 2 = x +2

If you have the slope and a point, you can plug in the x and y to get the value for b and then complete the equation.

Knowing a little can help a lot (to look things up) in math

Tutoring precalculus,

We started by looking at problems with sets of equations.

The first were sets of linear equations.

Others had quadratics. For one problem, if you recognized part of the equation was a perfect square, it made the problem easier.

Other times a single mistake like reversing a negative sign could cause problems later on, especially if done early on that means redoing a lot of work.

After the winter break he was a little rusty with a few things.

It’s important to be able to recognize the equations of parabolas, ellipses, and hyperbolas. If you know what something is, you can look up equations for it more easily.