Warm-Up Question. Solve each triangle. B. B. 10.8. 5. a. a. A. A. b. C. C. b. Definition of General Angles and Radian Measure. Trigonometric Ratios and Functions. Angles in Standard Position. Lesson: P.563. In a coordinate plane, an angle can be formed
Solve each triangle.
Definition of General Anglesand Radian Measure
Trigonometric Ratiosand Functions
In a coordinate plane, an angle can be formed
by fixing one ray, called the initial side, and
rotating the other ray, called the terminal side,
about the vertex.
An angle is in standard position if its vertex is at
the origin and its initial side lies on the positive
Draw an angle with the given measure in standard position.
Required Practice: P.5663, 4, 6, 7, 8, 9, 14
The angle and are coterminal because
their terminal sides coincide. An angle coterminal
with a given angle can be found by adding or
subtracting multiples of .
Draw an angle with the given measure in standard position. Then find one positive coterminal angel and one negative coterminal angle.
Required Practice: P.56715, 16, 17, 18
Find the circumference and area of below circle.
Area of Circle:
Find the arc length and area of below sector.
Area of Sector:
One radian is the measure of an angle in standard
position whose terminal side intercepts an arc of
length r. (Refer to the animation on the next slide.)
There are approximately 6.28 radian in a full circle,
or to be exact. Degree measure and radian
measure are therefore related by the equation
radians, or .
Convert to radians.
Convert to degrees.
Required Practice: P.5655, 6, 7, 8
The arc length s and area A of a sector with radius r
and central angle (measured in radians) are as
Find the arc length and area of a sector with the given radius r and central angle .
1) r = 4 in., 2) r = 15 cm,
Required Practice: P.56733, 37
Workbook P.116: 1, 4, 5
Workbook P.116 – 117: 6, 7, 8, 9, 10, 11, 13, 14