Trigonometric Ratios Geometry Sources Discovering Geometry 2008 by
Trigonometric Ratios Geometry Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson
Jan 4 - Monday Let’s Review!
Jan 4 - Monday Let’s Review!
Jan 4 - Monday Trigonometry � Trigon – triangle � Metria – measure � “Triangle Measurement” in Greek � Applications in Navigation, Surveying, Astronomy, etc.
Jan 4 - Monday What is a trigonometric ratio? TRIGONOMETRIC + RATIO Triangle Measurement + Comparison between quantities So what are we comparing in a trigonometric ratio? A trigonometric ratio expresses a comparison between the lengths of sides of a (right) triangle.
Jan 4 - Monday Trigonometric Ratio Example: Hypotenuse leg
Jan 4 - Monday Trigonometric Ratio � BUT HOW DO WE AVOID CONFUSION? � WHICH LEG ARE WE TALKING ABOUT? � Let’s have a reference. � Example: B Opposite leg A C Adjacent leg
Jan 4 - Monday Let’s Practice! (Opposite vs Adjacent) Z Y X
Jan 4 - Monday �Let’s consider similar triangles. Tangent Ratio 60 o 1 60 o 2 60 o 3
Jan 5 - Monday Tangent Ratio � The ratio of the length of the opposite leg to the length of the adjacent leg of an acute angle in a right triangle remains constant. � This is called the TANGENT RATIO. � Example: a A b
Jan 5 - Monday Exercise B � Given: 5 A 3 4 C
Jan 5 - Monday Exercise � Given: B 16 A 54 o x C
Jan 5 - Monday Exercise Use your calculator!
Jan 5 - Monday Sine and Cosine Ratio � Sine Ratio = � Cosine Ratio = h A b a
Jan 5 - Monday Take Note!
Jan 5 - Monday Try this! � Given: x Q R y z S
Jan 5 - Monday More Exercises � Determine the unknown.
Jan 5 - Monday More Exercises � Determine the unknown.
Jan 5 - Monday Try this! � Given: Q 4 R 550 a b S Solve for a and b.
Jan 5 - Monday More Exercises � Solve for the unknowns. Express in simplest form.
Jan 5 - Monday More Exercises � Solve for the unknowns. Express in simplest form.
Jan 5 - Monday More Exercises � Solve for the unknowns. Express in simplest form.
Jan 5 - Monday More Exercises � Solve for the unknowns. Express in simplest form.
Jan 6 - Tuesday Finding measures of angles: � Given: T R 25 14 S
Jan 6 - Tuesday More Exercises � Determine the angle measures. Express each to the nearest degree.
Jan 6 - Tuesday More Exercises � Determine the angle measures. Express each to the nearest degree.
Jan 6 - Tuesday More Exercises � Determine the angle measures. Express each to the nearest degree.
Jan 6 - Tuesday Try this! � Given: n 460 16 Solve for m, n, and p. 11 m p
Jan 6 - Tuesday More Exercises
Jan 6 - Tuesday More Exercises Solve for h.
Jan 6 - Tuesday More Exercises Solve for y.
Jan 6 - Tuesday More Exercises � Solve for the unknowns.
Jan 6 - Tuesday More Exercises � Solve for the unknowns.
Jan 6 - Tuesday More Exercises � Solve for the unknowns.
Jan 6 - Tuesday More Exercises � Solve for the unknowns.
Jan 6 - Tuesday More Exercises � Solve for the unknowns.
Jan 6 - Tuesday More Exercises
Jan 6 - Tuesday More Exercises � WITHOUT A CALCULATOR, Complete the table. What do you observe? Can you explain why the answers are such ?
More Exercises
More Exercises
- Slides: 40