About This Chapter
Geometry and Trigonometry in Calculus
Like many academic pursuits, math is a subject where what you learn today is based on what you learned yesterday. Rarely does your knowledge of the topic stand alone; you can't take a class in advanced math before you learn how to add, subtract, multiply and divide. With that in mind, these lessons explain how basic math skills play a part in advanced mathematical concepts - and this course will help you to brush up on those skills.
These lessons will cover how to solve by visualizing problems; you'll see how to apply graphical and hands-on approaches to questions as you proceed through this course. You'll also cover some basic volume calculations by going over how to calculate the volume of spheres, pyramids and other basic shapes.
From here, the lessons will lead you into discussion of an important piece of mathematical knowledge - the Pythagorean Theorem. You'll study how to apply the Pythagorean Theorem to find the distance between points and you'll learn to apply this theorem to both simple and advanced concepts.
As the lessons continue, you'll look at basic trigonometric functions like sine and cosine. You'll see how to graph them and how to describe them on right triangles.
The main point of these lessons is to be sure that you remember the important basics that you probably learned in past mathematics courses. You'll look over some key concepts that will be used in advanced level math and can prepare you to move forward in your studies.
1. How to Solve Visualizing Geometry Problems
A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.
2. How to Calculate the Volumes of Basic Shapes
Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?
3. Volume of a Frustum of Pyramids & Cones
Knowing how to calculate the volume of a cone or a pyramid leads to equations for the volume of a frustum. In this lesson, we derive two equations for calculating the volume of frustums.
4. Volume Formulas for Pyramids, Prisms, Cones & Cylinders
Pyramids, prisms, cones, and cylinders are three-dimensional objects that show up everywhere in the world around us. This lesson teaches us how to find the volume of these objects and look at the relationships between their volumes.
5. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
6. Trigonometry: Sine and Cosine
Learn an easy trick to help you solve trigonometry problems, including problems with sine, cosine and inverse trig functions. At the end of this lesson, you'll know what SohCahToa means and how to use it.
7. Trigonometry and the Pythagorean Theorem
Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.
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Other chapters within the Math 104: Calculus course
- Graphing and Functions
- Vectors in Calculus
- How to Use a Scientific Calculator
- Rate of Change
- Calculating Derivatives and Derivative Rules
- Graphing Derivatives and L'Hopital's Rule
- Applications of Derivatives
- Area Under the Curve and Integrals
- Integration and Integration Techniques
- Integration Applications
- Differential Equations
- Studying for Math 104