Download Unit 6 Lesson 3 Do Now From a point on the floor the angle of

Name: _______________________
Period # _____
Unit 6 Lesson 3 Do Now
From a point on the floor the angle of elevation to the top of a door is 47°, while
the angle of elevation to the ceiling above the door is 61°. The ceiling is 12 ft
above the floor. Find the vertical dimension of the door.
Diagram
Solution
Name: _______________________
Period # _____
Unit 6 Lesson 3 Do Now
From a point on the floor the angle of elevation to the top of a door is 47°, while
the angle of elevation to the ceiling above the door is 61°. The ceiling is 12 ft
above the floor. Find the vertical dimension of the door.
Diagram
Solution
Pre-Calculus Honors
Book Reference 4.3
Unit 6 Lesson 3: Evaluating trig functions without using a calculator and finding
trig ratios given one ratio
Objective: _____________________________________________________________
Definitions
Mark up the following definitions. You will label the
following properties on the diagram using the verbal on
the right.
Verbal
1. Initial side: The beginning position of the ray
2. Terminal side: The final position of the ray.
3. Vertex: The endpoint of the initial side and the terminal
side
4. Measure of the angle: The rotation from the initial side
to the terminal side.
5. Positive angles: Generated by a counterclockwise
rotation.
6. Negative angles: Generated by a clockwise rotation
7. Reference angle θ : Angle in between the terminal side
and the x-axis.
8. Coterminal angles: Two angles in the expanded angle
measurement system that have the same initial and
terminal side, but different amounts of rotation.
9. Standard position: In the Cartesian plane, the vertex of
Let θ be the acute angle in standard position whose
terminal side contains (8, -4). Find the six trigonometric
functions of θ.
the angle is the always the origin and the initial side of
the angle is always the x-axis.
Diagram
Draw the angle in standard position. Label the initial
side, terminal side, reference angle θ , the x, the y, and
the r (radius).
Six Trig Functions of θ
sin θ =
cscθ =
cosθ =
secθ =
tan θ =
cot θ =
2. Group Practice: Generalizing Rules for Evaluating Trig Functions
Example Quadrant 1
Example Quadrant 2
Let θ be the acute angle in standard position whose
Let θ be the acute angle in standard position whose
terminal side contains (2, 5). Find the exact value, in
terminal side contains (-3, 6). Find the exact value, in
simplest radical form, of the six trigonometric
simplest radical form, of the six trigonometric
functions of θ.
functions of θ.
sin θ =
cscθ =
sin θ =
cscθ =
cosθ =
secθ =
cosθ =
secθ =
tan θ =
cot θ =
tan θ =
cot θ =
Example Quadrant 3
Let θ be the acute angle in standard position whose
terminal side contains (-4, -7). Find the exact value, in
simplest radical form, of the six trigonometric
functions of θ.
Example of Quadrant 4
Let θ be the acute angle in standard position whose
terminal side contains (2, -7). Find the exact value, in
simplest radical form, of the six trigonometric
functions of θ.
sin θ =
cscθ =
sin θ =
cscθ =
cosθ =
secθ =
cosθ =
secθ =
tan θ =
cot θ =
tan θ =
cot θ =
Making Generalizations:
1.) Describe which trig functions are always positive in each quadrant.
Quadrant 2
Quadrant 1
Quadrant 3
Quadrant 4
2.) Re-write the six trig functions in terms of x, y, and r.
sin θ =
cosθ =
tan θ =
cscθ =
Pre-Calculus Honors Homework: Finish classwork
secθ =
cot θ =
(Long Block Only) Pre-Calculus Honors Homework PG 381 (3-11 odd, 17-20, 43, 45,
47)