These STEM Precalculus lessons are a continuation of previous foundations from NASA’s STEM Algebra 1/2 and Geometry lessons. Students use functions, equations, and limits to express generalizations and to analyze and understand a broad variety of mathematical relationships. These Precalculus STEM lessons teach studens how to use functions to represent not only algebraic and geometric situations, but those involving probability, statistics and trigonometry, as well as calculus. Some of these precalculus lessons require students to use the Texas Instruments Nspire calculator. Also, for additional precalculus lessons, texts and videos, take a look at 165 Precalculus Videos with Texts, Exercises and Reviews.

1. 7 Precalculus STEM Lessons from NASA
November 26, 2021
7 Precalculus STEM Lessons from NASA
These STEM Precalculus lessons are a continuation of previous foundations from NASA’s STEM
Algebra 1/2 and Geometry lessons. Students use functions, equations, and limits to express
generalizations and to analyze and understand a broad variety of mathematical relationships. These
Precalculus STEM lessons teach studens how to use functions to represent not only algebraic and
geometric situations, but those involving probability, statistics and trigonometry, as well as calculus.
Some of these precalculus lessons require students to use the Texas Instruments Nspire calculator. Also,
for additional precalculus lessons, texts and videos, take a look at 165 Precalculus Videos with Texts,
Exercises and Reviews.
SPACE VECTORS
Key Topics: Vector addition
High accuracy radars at NASA Dryden Flight Research Center are used to track and relay the position of
the International Space Station and other research vehicles. In this activity, students will use spherical
coordinates and vector addition to find position coordinates of the space shuttle with respect to the
Earth’s center and Dryden Flight Research Center.
Students will
• transform spherical coordinates to Cartesian coordinates;
• represent 3D vectors in terms of i, j, and k; and
• perform vector addition operations.
Lesson Files:
• Space Vectors Educator Edition
• Space Vectors Student Edition
• Spherical Coordinate Systems
• Download: Google Earth
EARTH CAN YOU HEAR ME NOW?
Key Topic: Trigonometric Functions, Graphs of Trigonometric Functions
Exploring space is a complex endeavor. Future destinations include Mars. Students will investigate,
analyze and model the communication time lag between Earth and Mars. Transmitting a message
between Earth and Mars could take up to 20 minutes because of the distance between the two planets.
Students will
• Use trigonometric functions to model periodic behavior or real life data;
• Make predictions based on the properties of a function;

2. • Graph a sine curve; and
• determine the domain and range of functions using graphs and tables.
Prerequisites: Students should have prior knowledge of plotting data on a coordinate plane, of solving
equations, and of key characteristics of a sinusoidal function and the parent function, f(x)=sinx.
Lesson Files:
• Earth Can You Hear Me Now Educator Edition
• Earth Can You Hear Me Now Student Edition
• Video: Spirit – Six Years of Roving Mars (4:54 min, 32.1mb)
• Video: Mars and Earth Orbit Animation (3 secs, 299kb)
COMMUNICATIONS AND THE LUNAR OUTPOST
Key Topic: Pythagorean Theorem, arc length, inverse tangent
Students will apply mathematics formulas to calculate various geometric measures in the relationships
between the height of a lunar communication tower and the tower’s communications range.
Students will
• use algebraic properties to solve equations for a given variable;
• apply formulas to calculate various geometric measures; and
• analyze data to determine a solution to a real life problem.
Prerequisites: Prior to this activity, students should have had experiences applying formulas. Students
should be familiar with using calculators in evaluating formulas and have a basic knowledge of circles,
trigonometric functions, and point of tangency.
Lesson Files:
• Communications and the Lunar Outpost Educator Edition
• Communications and the Lunar Outpost Student Edition
THE LUNAR LANDER – ASCENDING FROM THE MOON
Key Topic: Application of trigonometric functions
Students will apply trigonometric functions when using data from the liftoff of the Lunar Lander from
the Moon’s surface.
Students will
• use trigonometric function rules to solve problems; and
• graph and analyze functions to determine a relationship between two variables.
Prerequisites: Students should have a good knowledge of right triangle trigonometry and how to solve
problems using trigonometric functions and inverse trigonometric functions. Students should also be
able to manipulate and evaluate functions.
Lesson Files:
• Lunar Lander Educator Edition
• Lunar Lander Student Edition

3. THE ROBOTIC ARM
Key Topics: Trigonometric functions
In April 2001, the International Space Station (ISS) was equipped with a robotic arm built by the
Canadian Space Agency. Canadarm2 has been instrumental in the assembly of the ISS modules as well as
movement of supplies and equipment—even astronauts. In this activity, students will study the
movement and mechanics of the robotic arm using their knowledge in geometry and precalculus.
Students will
• manipulate a two-dimensional simulation of the robotic arm to capture an astronaut;
• use trigonometric functions to determine distances spanned; and
• determine the relationship between angles of deflection and angles of rotation of the robotic arm.
Lesson Files:
Note: This activity requires the use of TI-Nspire technology to be used successfully.
Files for use with the TI-Nspir calculator:
• The Robotic Arm TI-Nspire Educator Edition
• The Robotic Arm TI-Nspire Student Edition
• Note: The following files are specific for Texas Instrument Nspire calculators:
• The Robotic Arm TI-Nspire Document (TNS)
• The Robotic Arm TI-Nspire Solution Document (TNS)
• Video: ISS Update: Capturing a Dragon (9:00 min, 19.5mb)
SIMULATING WEIGHTLESSNESS
Key Topics: Parametric and parabolic equations
The C-9 jet is one of the tools utilized by NASA to simulate the gravity, or reduced gravity, that
astronauts feel once they leave Earth. The C-9 jet flies a special parabolic pattern that creates several
brief periods of reduced gravity. In this activity, students will study the flight pattern of NASA’s C-9 jet
using their knowledge of pre-calculus and parametric equations.
Students will
• understand and write parametric equations that model the path of NASA’s C-9 jet;
• determine the distance and height of a projectile after t seconds;
• analyze given parameters to solve a real-life problem situation;
• find the maximum time and distance of one parabolic maneuver and interpret their significance;
and
• use time as a parameter in parametric equations.
Lesson Files:
Note: This activity requires the use of TI-Nspire technology to be used successfully.
Files for use with the TI-Nspire calculator:
• Simulating Weightlessness TI-Nspire Educator Edition
• Simulating Weightlessness TI-Nspire Student Edition
• Note: The following files are specific for Texas Instrument Nspire calculators:

4. • Simulating Weightlessness TI-Nspire Document
• Simulating Weightlessness TI-Nspire Solution Document
• Video: NASA Reduced Gravity Student Flight Opportunity (13:42 min, 36.8mb)
RENDEZVOUS FOR TWO
Key Topics: Circles and Ellipses
Students will describe the circular orbits of the space shuttle and the International Space Station by
writing the equations of the orbits using distance data from the center of the Earth. Students will also
predict the trajectory of the space shuttle as it rendezvous’ with the International Space Station using the
properties of an ellipse.
Students will
• write an equation of an ellipse in standard form;
• calculate the lengths of semi-major and semi-minor axes;
• calculate the distance of the foci;
• calculate eccentricity; and
• write an equation of a circle.
Lesson Files:
Files for use with the TI-Nspire calculator:
• Rendezvous For Two TI_Nspire Educator Edition
• Rendezvous For Two TI_Nspire Student Edition
• Note: The following file is specific for Texas Instrument Nspire calculators:
• Rendezvous For Two TI_Nspire Document (TNS)
• Video: Real World: Calculating Shuttle Launch Windows (6.5mb, 25.2mb)

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