{"id":145,"date":"2020-04-07T16:56:17","date_gmt":"2020-04-07T23:56:17","guid":{"rendered":"http:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=145"},"modified":"2024-07-19T16:22:45","modified_gmt":"2024-07-19T23:22:45","slug":"trigonometric-concepts-unit","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-students\/trigonometric-concepts-unit\/","title":{"rendered":"Trigonometric Concepts Unit"},"content":{"rendered":"\n

Two students, Mary and Claire, investigate angle measure and the sine function. They begin by investigating how to measure angles in a variety of ways. They explore how to measure these angles in degrees, non-standard units, and radians. Next, they investigate the sine function. They explore how the function relates two quantities as they co-vary, and how to graph the function. Finally, they investigate how to manipulate the graph of the sine function to model climate data.<\/p>\n\n\n\n

Lesson 1: Measuring Angle Openness<\/a><\/h5>\n\n\n\n

Mary and Claire explore what it means for one angle to be more open than another. They also investigate how to measure that openness using both degrees and non-standard units.<\/p>\n\n\n\n

Lesson 2: Making Sense of Angles as Rotations<\/a><\/h5>\n\n\n\n

Mary and Claire explore how to create and measure angles that represent the amount an object has rotated. They measure the angles using both degrees and a non-standard unit of measure. They then reflect on what those measurements mean in terms of the rotation.<\/p>\n\n\n\n

Lesson 3: Investigating the Relationship between Arc Length and the Angle of Rotation<\/a><\/h5>\n\n\n\n

In this lesson, Mary and Claire investigate the relationship between an angle measure and the length of the arc that it cuts out in a circle<\/p>\n\n\n\n

Lesson 4: Measuring Angles Using Radians<\/a><\/h5>\n\n\n\n

In this lesson, the students will explore the radian as a unit of measure. They will estimate the measure in radians of arcs, and also help us think about the connection between radians and degrees. <\/p>\n\n\n\n

Lesson 5: Exploring Covariation on a Unit Circle<\/a><\/h5>\n\n\n\n

In this lesson, Mary and Claire think about how an object\u2019s height changes in relation to its angle of rotation as it moves along a circular path. They also explore what happens to the changes in height as the object moves. They explore how this relates to circular motion along different sizes of circles.<\/p>\n\n\n\n

Lesson 6: Creating a Graph of the Sine Function<\/a><\/h5>\n\n\n\n

In this lesson, Mary and Claire develop a graph of the sine function. They grapple with how to scale the x- and y-axes so they can show the relationship between an object\u2019s angle of rotation and its height above the midline of a circle as it travels along the circumference of that circle. <\/p>\n\n\n\n

Lesson 7: Transforming the Sine Function<\/a><\/h5>\n\n\n\n

In this lesson, Mary and Claire modify the sine function to give the height above the ground of a student named April as she travels on a Ferris wheel.<\/p>\n\n\n\n

Lesson 8: Modeling Climate Data with a Sinusoidal Function<\/a><\/h5>\n\n\n\n

In this lesson, Mary and Claire transform the sine function using sliders to model temperature data. They use their models to predict future patterns in temperature.<\/p>\n\n\n\n

<\/span>\"Claire
\n
Who Are Claire
and Mary?<\/a>
<\/h5>\n<\/div><\/div>\n\n\n\n

<\/p>\n\n\n\n

\n
Home<\/a><\/div>\n\n\n\n
Units<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Two students, Mary and Claire, investigate angle measure and the sine function. They begin by investigating how to measure angles in a variety of ways. They explore how to measure these angles in degrees, non-standard units, and radians. Next, they investigate the sine function. They explore how the function relates two quantities as they co-vary, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":149,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-145","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/145","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=145"}],"version-history":[{"count":19,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/145\/revisions"}],"predecessor-version":[{"id":7504,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/145\/revisions\/7504"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/149"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}