Arclength, radians to degrees and opposite, Tutoring Geometry

Focused mostly on arclength.

The equation used is that for circumference. And then you figure out the fraction of the circle. Which could be any amount, sometimes it was 1/2 for a semicircle.

You can convert between radians and degrees using a conversion factor, just like you would for cm to inches, etc.

Reviewed some common angles in radians, which are often fractions of pi.

2r is the diameter. So if the diameter is given, you can substitute it for 2r.

Inverse Trig Functions “Unlock” the Arguments of Trig Functions, Tutoring Geometry

We started by using SOHCAHTOA.

One mistake was not including an argument of the function. Sin, cos, tan do not mean anything without an argument. So sinx, cosx, tanx, etc.

Went over some ways to manipulate algebraic expressions.

Talked about how the inverse trig functions reverse the action of a trig function.

They are somewhat like a key which unlocks a box which holds the argument of a trig function and all that is left is the argument.

Reminded about using the degree symbol • and using units when applicable.

Used the Pythagorean Theorem a few times.

Briefly talked about the reciprocals of trig functions.

“How do I find the angle of a right triangle knowing the ratios of the sides?”

You can use an inverse trig function of the ratio using SOHCAHTOA. Then you can subtract the two known angles from 180° to get the remaining angle.

“What is the compliment of a 32 degree angle?”

Here’s a diagram to show what a complement means for angles.

If you have two angles that add up to 90° then they are said to be “complementary”.

One of the angles in this example is 32°.

“How do I find the sin of any angle?”

How do I find the sin of any angle?

For example, if I wanted to find the sin of 30 or 10, how would I go about doing that.

You need to know whether the angle is specified in degrees or radians since there are two systems for measuring degrees.

At that point, if you can use a calculator, you might press 30 then the sin button.

Or for a different sort of calculator you would input sin(30) then press enter.

Make sure that you are in degree mode or radian mode depending on what you’re working with.

Without a calculator, some angles are easier to find than others. For example, 30°, 45°, etc are triangles with well known ratios of their sides. So you can think of SOHCAHTOA.

For angles related to those, you can use things like half angle formulas.

From the two examples you gave, sin(30°) = 0.5. sin(10°), I’m not sure offhand.

There are tables you can look up values. If you end up looking up a certain value a lot, you may remember it.

“Why are there 9 square feet in 1 square​ yard?”

Since a yard is equal to three feet. Here is a way to see it visually.

“What is the name of a triangle with one round side?”

What is the name of a triangle with one round side?

Kind of like a piece of cake which has two straight sides and one round side. Or a slice of pizza.

-Quora

It has properties of a circle with the round part, since it has a section of the circumference. And the area of the shape is a part of an entire circle.

Surface Area of a Regular Pentagonal Pyramid

regular_pentagonal_prism_surface_area

Tutoring, Reviewing for Geometry/Algebra Final

We started by graphing the overlap of two inequalities. If the inequalities are less than or greater than you use a dotted line since they do not include the values on the line.

At that point I sketch horizontal lines either above or below one line and vertical lines above or below the second line and then you can see the overlap easily.

We graphed some parabolas, using the equation of for the vertex and showing the axis of symmetry.

Did a few problems with point slope and slope intercept form.

A few problems with long division and synthetic division.

And ended by looking at some volumes of 3D shapes. Talked for a minute about how you can see if an equation describes a volume or an area. Basically looking for whether something is 3D or 2D.

Circle Circumference and Area Formulas

circle_circumference_area_equations_formulas

Formulas for area and circumference of a circle.