MATH 108 at the University of Maryland Global Campus is the second course in the MATH 107 and MATH 108 series, with MATH 107 as its prerequisite. UMGC describes an introduction to trigonometric functions, identities and equations and their applications.
It also covers analytical geometry and conic sections, systems of linear equations, matrices, sequences and series. Students find the identities and proofs the most demanding part, because success depends on choosing a sensible first move.
Course at a Glance
| Item | Details |
|---|---|
| University | University of Maryland Global Campus |
| Course code | MATH 108 |
| Credits | 3 |
| Level | Undergraduate |
| Prerequisite | MATH 107 |
| Credit rule | Credit for only one of MATH 108 or MATH 115 |
| Typical work | Problem sets on trigonometry, vectors and conics (general; check your term) |
What MATH 108 Covers
| Area | Skill |
|---|---|
| Trigonometric functions | Definitions, unit circle and graphs |
| Identities and equations | Proving identities and solving trigonometric equations |
| Solving triangles | Laws of sines and cosines |
| Vectors | Operations and magnitude |
| Analytical geometry | Conic sections |
| Systems, matrices, sequences and series | Further algebraic tools |
Key Concepts Explained
Law of Sines
In any triangle, a / sin A = b / sin B.
Example: If a = 7, A = 30 degrees and B = 45 degrees, then b = 7 x sin 45 / sin 30 = 7 x 0.7071 / 0.5, about 9.90.
Proving Identities
Work on one side only and rewrite it until it matches the other. Start by using sin^2 + cos^2 = 1 or by writing everything in sines and cosines.
Trigonometric Equations
To solve sin x = 1/2 on 0 to 360 degrees, use the reference angle of 30 degrees. Sine is positive in quadrants I and II, so x = 30 or 150 degrees.
Typical Assignments and How to Approach Them
| Assignment type | What it tests | How to approach it |
|---|---|---|
| Identity proofs | Strategy and algebra | Convert to sine and cosine, combine fractions, simplify one side |
| Equation sets | Solving over a range | Find the reference angle, then place it in the correct quadrants |
| Triangle problems | Applying laws of sines and cosines | Sketch and label before choosing the law |
| Vector and conic tasks | Geometry with algebra | Write the standard form and read off the key features |
Unit Circle Essentials
Memorize the sine and cosine at 0, 30, 45, 60 and 90 degrees, then use symmetry for the other quadrants. Most identity and equation problems depend on these values.
| Angle | sin | cos |
|---|---|---|
| 30 degrees | 1/2 | square root of 3 over 2 |
| 45 degrees | square root of 2 over 2 | square root of 2 over 2 |
| 60 degrees | square root of 3 over 2 | 1/2 |
More Worked Examples
Law of cosines: with sides 5 and 7 and an included angle of 60 degrees, c^2 = 25 + 49 - 2(5)(7)cos 60 = 74 - 35 = 39, so c is about 6.24.
Identity: show (1 - cos^2 t)/sin t = sin t. Replace 1 - cos^2 t with sin^2 t, so the left side is sin^2 t / sin t = sin t.
Vector: The magnitude of (3, 4) is the square root of 9 + 16, which is 5.
Conic Sections at a Glance
Conic sections come from slicing a cone. Each has a standard form that reveals its key features, so learning to complete the square is the main skill.
| Conic | Standard form (centered at origin) | What to read off |
|---|---|---|
| Circle | x^2 + y^2 = r^2 | Radius |
| Ellipse | x^2/a^2 + y^2/b^2 = 1 | Semi-axes a and b |
| Hyperbola | x^2/a^2 - y^2/b^2 = 1 | Vertices and asymptotes |
| Parabola | y = a x^2 | Vertex and direction |
A Short Self-Test
Work these without notes. The answers should come from the unit circle and identities, not from a calculator.
- State sin, cos and tan of 45 degrees.
- Solve cos x = -1/2 for x between 0 and 360 degrees.
- Prove that tan t cos t = sin t.
- Find the magnitude of the vector (5, 12).
- Identify the conic x^2/9 + y^2/4 = 1.
Systems and Matrices
The later part of the course returns to algebra. A system of linear equations can be written as a matrix and solved by row operations, which is a tidy way to handle three or more unknowns. Practice writing the augmented matrix, reducing it step by step, and reading the answer, and always check by substituting back into the original equations.
Where Students Get Stuck
- Ambiguous triangles. The law of sines can give two solutions; check both.
- Degrees versus radians. Check your calculator mode.
- Identity proofs. Do not treat both sides as an equation to manipulate.
- Quadrant signs. Check the sign of each function.
Study Tips for MATH 108
- Make a one-page identity sheet and rewrite it from memory.
- Sketch every triangle problem.
- Try identities in sines and cosines first.
- Test numerical values to check suspected identities.
How We Help with MATH 108
Send the problem set, your notes and your working. A maths tutor can explain each method, prepare fully worked solutions to study from, or check your steps.
GradeEssays is independent and not affiliated with University of Maryland Global Campus. Our work is a study and reference aid: use it to understand the method, then complete and submit your own work under UMGC's academic integrity policy.
Every order is written from scratch, comes with free revisions within the scope of your original request, and is refunded in full if it is late.
Get MATH 108 Explained Clearly
Share the problems and your attempts. A maths tutor prepares fully worked solutions.
Start My MATH 108 HelpFree revisions · Full refund if late · Written from scratch for your order
Frequently Asked Questions
UMGC lists MATH 107.
Trigonometric functions, identities and equations, analytical geometry and conic sections, systems of linear equations, matrices, sequences and series, and vector operations.
UMGC says students may receive credit for only one of MATH 108 or MATH 115.
MATH 140 Calculus I lists MATH 108 or MATH 115 as its prerequisite.
Some facts must be memorized, but identity proofs and applications need reasoning.
Yes. We review each step and explain corrections.