Chapter 10 - NCPN

Trigonometric Functions
and Identities
Why should I learn this
Trigonometry is about right angles and angle relationships. Many real‐world
problems that are solved using trigonometric functions relate to indirect
measurement. The topics of this chapter incorporate previously learned skills,
such as using the Pythagorean Theorem and simplifying radicals.
Trigonometric functions and relationships are the underlying mathematics used
in occupations that deal with distance and measurement.
• Air Traffic Controllers interpret data processed by machines that are
programmed using trigonometric functions.
• Cartographers use trigonometry to indirectly measure distances and
verify that their maps are accurate.
• Musicians, especially those who play stringed instruments, produce
harmonic tones that are based on variations of the sine function.
In this chapter, you will use the trigonometric ratios to interpret and solve
problems. You will also learn to convert measurements between degrees
and radians.
Project Idea: Shadow to Shadow
When you are outside on a sunny day, you cast a shadow. The length
of the shadow depends on the time of day. The ratio of the height of
a person to the length of the shadow cast is equivalent to the ratio of
another person or object and its shadow length. Both measurements
must be taken at the same time of day from the same place.
Select an object, such as a tree or a flag pole, on the school
grounds. Work with a partner to determine and verify the
height of that object using indirect measurement. Find the
length of shadows cast by you and your selected object.
Then use your height and measurements gathered to find
the height of your object. Your partner should make the
same measurements and computations using his or her
height and shadow to find the height of the object. You
can verify the height of your object by comparing results
with your partner.
Chapter 10 Trigonometric Functions and Identities 435