Midterm Exam Would the following students please come to the board and share your methods of solving with solutions:

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Presentation transcript:

Midterm Exam Would the following students please come to the board and share your methods of solving with solutions:

Trigonometry Enjoy!

Section 4.1 Angles and their measures -Convert from degrees to radians and vice versa -Find arc length -Solve problem with angular speed

DMS DMS stands for Degree-Minutes-Seconds, and is a type of degree measurement where:

Converstions from DMS to degrees and vice versa DMS to Degree Degree to DMS

Your turn. Convert from degrees to DMS Convert from DMS to degrees

What is 1 radian? A central angle of a circle has a measure of 1 radian if it intercepts an arc with the same length as the radius.

Definition of a Radian the radian measure of the angle is the ratio of the length of the intercepted arc to the radius of the circle where θ is a central angle, s is the intercepted arc, and r is the radius

Finding a conversion factor At 360 degrees the radian measure would be the ratio of the circumference to the radius

So our conversion factors are: From radians to degrees From degrees to radians

Try these How many radians are in 120°? Convert π/6 from radians to degrees. Change 7π/9 to degrees.

Arc Length Formulas For Radian Measure For Degree Measure

Pizza Pi Time! Find the perimeter of a 50° slice of a large (diameter = 14 in.) pizza.

Let’s race! It takes 10 identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track?

Rollin’ rollin’ rollin’ Chuck’s truck has wheels 36 inches in diameter. If the wheels are rotating at 360 rpm (revolutions per minute), find the truck’s speed in miles per hour.