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 0 sin = ± 1+ cose Ꮎ 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

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Module 11, Half-Angle Identities Assignment
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
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
12 ft
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
Transcribed Image Text:Module 11, Half-Angle Identities Assignment 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 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 12 ft 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
5. Carry out your plan from question 4 and state the height of each rectangle.
6. How much wire will Marcus need to secure his latticework to the ground? Round to the
nearest foot and explain how you found your answers.
Transcribed Image Text:5. Carry out your plan from question 4 and state the height of each rectangle. 6. How much wire will Marcus need to secure his latticework to the ground? Round to the nearest foot and explain how you found your answers.
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