In this module you have worked with many different trigonometric identities. These identities can be helpful for making precise calculations. For example, you can use identities to find the lengths of the sides of a triangle when the angle measure in standard position is not listed on the unit circle. Most recently you have learned about double-angle and half-angle identities. These are special cases of the sum and difference formulas for sine and cosine. Consider the half-angle identities shown as you work through the scenario below. Sine Half-Angle Identity Cosine Half-Angle Identity 1- cose 1+ cose cos-= + sin 2 Marcus is a craftsman and artist. He uses the knowledge he has gained as an engineering student to create custom pieces. For his current project, he is making a large, intricate, 3-dimensional latticework that will be placed next to the marker which welcomes people to his city. He has the work on the lattice completed. It consists of two long rectangles, such that the bottom rectangle will act as a base for the top rectangle. Together the two rectangles are 12 feet tall. In order to help the latticework remain vertical, Marcus will attach two wires to each side of the piece, and affix them to the ground at a point that is exactly 9 feet from the base of the artwork, as shown in the illustration. The measure of the angle of elevation to the top of the base is one-half the measure of the angle of elevation to the top of the latticework. 12 ft Use this information and what you know about trigonometric ratios and identities to help you explore the questions below. 9 ft 1. Can you use the given information to calculate the measure of the angle of elevation to the top of the latticework? If so, find the angle measure to the nearest degree. Show your work. If not, explain why not and what information is needed.
In this module you have worked with many different trigonometric identities. These identities can be helpful for making precise calculations. For example, you can use identities to find the lengths of the sides of a triangle when the angle measure in standard position is not listed on the unit circle. Most recently you have learned about double-angle and half-angle identities. These are special cases of the sum and difference formulas for sine and cosine. Consider the half-angle identities shown as you work through the scenario below. Sine Half-Angle Identity Cosine Half-Angle Identity 1- cose 1+ cose cos-= + sin 2 Marcus is a craftsman and artist. He uses the knowledge he has gained as an engineering student to create custom pieces. For his current project, he is making a large, intricate, 3-dimensional latticework that will be placed next to the marker which welcomes people to his city. He has the work on the lattice completed. It consists of two long rectangles, such that the bottom rectangle will act as a base for the top rectangle. Together the two rectangles are 12 feet tall. In order to help the latticework remain vertical, Marcus will attach two wires to each side of the piece, and affix them to the ground at a point that is exactly 9 feet from the base of the artwork, as shown in the illustration. The measure of the angle of elevation to the top of the base is one-half the measure of the angle of elevation to the top of the latticework. 12 ft Use this information and what you know about trigonometric ratios and identities to help you explore the questions below. 9 ft 1. Can you use the given information to calculate the measure of the angle of elevation to the top of the latticework? If so, find the angle measure to the nearest degree. Show your work. If not, explain why not and what information is needed.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
Half-
Transcribed Image Text:In this module you have worked with many different trigonometric identities. These identities
can be helpful for making precise calculations. For example, you can use identities to find the
lengths of the sides of a triangle when the angle measure in standard position is not listed on the
unit circle.
Most recently you have learned about double-angle and half-angle identities. These are special
cases of the sum and difference formulas for sine and cosine.
Consider the half-angle identities shown as you work through the scenario below.
Sine Half-Angle Identity
Cosine Half-Angle Identity
1- cose
1+ cose
sin
= +
Cos
= ±
2
2
Marcus is a craftsman and artist. He uses the
knowledge he has gained as an engineering student to
create custom pieces. For his current project, he is
making a large, intricate, 3-dimensional latticework
that will be placed next to the marker which welcomes
people to his city. He has the work on the lattice
completed. It consists of two long rectangles, such that
the bottom rectangle will act as a base for the top
rectangle. Together the two rectangles are 12 feet tall.
\12 ft
In order to help the latticework remain vertical, Marcus
will attach two wires to each side of the piece, and affix
them to the ground at a point that is exactly 9 feet from the
base of the artwork, as shown in the illustration. The
measure of the angle of elevation to the top of the base is
one-half the measure of the angle of elevation to the top of
the latticework.
Use this information and what you know about
trigonometric ratios and identities to help you explore the
questions below.
9 ft
1. Can you use the given information to calculate the measure of the angle of elevation to the top
of the latticework? If so, find the angle measure to the nearest degree. Show your work. If not,
explain why not and what information is needed.
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