## PreCalculus II - MTH 162 at Northern Virginia Community College

https://courses.vccs.edu/colleges/nova/courses/MTH162-PreCalculusII

Effective: 2022-03-31

### Course Description

Presents trigonometry, trigonometric applications including Law of Sines and Cosines and an introduction to conics. Credit will not be awarded for both MTH 162: Precalculus II and MTH 167: Precalculus with Trigonometry or equivalent. This is a Passport and UCGS transfer course.

Lecture 3 hours. Total 3 hours per week.

3 credits

The course outline below was developed as part of a statewide standardization process.

### General Course Purpose

The general purpose of this one-semester course, in conjunction with Precalculus I, is to prepare students for the skills and level of rigor needed for successful study in a sequence of courses in calculus with analytic geometry.

### Course Prerequisites/Corequisites

Prerequisites: Placement or completion of MTH 161: Precalculus I or equivalent with a grade of C or better

### Course Objectives

- Trigonometric Functions
- Identify angles in standard form in both degree and radian format and convert from one to the other.
- Find the arc length.
- Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry.
- Use reference angles to evaluate trig functions.
- Find the value of trigonometric functions of angles using a calculator.
- Use fundamental trigonometric identities to simplify trigonometric expressions.
- Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts.
- Use trig functions to model applications in the life and natural sciences.
- Analytic Trigonometry
- Use the fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities.
- Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions.
- Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions.
- Solve trigonometric equations over restricted and non-restricted domains.
- Applications of Trigonometry
- Solve right triangles and applications involving right triangles.
- Use the Law of Sines and Cosines to solve oblique triangles and applications.
- Conics
- Identify the conic sections of the form:Ax^2+By^2+Dx+Ey+F=0.
- Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin.
- Identify essential characteristics unique to each conic.
- Graph equations in conic sections, centered both at the origin and not at the origin.
- Solve applications involving conic sections.
- Sequences and Series (Optional unit at the discretion of the department, not required for transfer.)
- Identify the terms of geometric sequences.
- Find a particular term of geometric sequence.
- Determine the formula for the an term of geometric sequences.
- Find the sum of first n terms of finite geometric series.
- Find the sum of infinite geometric series.
- Introduce arithmetic concepts as time allows.

### Major Topics to be Included

- Trigonometric Functions
- Analytic Trigonometry
- Applications of Trigonometry
- Conics