Download Lesson 5.3 Notes

Bell Work
R
Find the 6 trig functions for
<R.
22 cm
S
14 cm
sin R =
csc R =
cos R =
sec R =
tan R =
cot R =
T
5-3
Trigonometric Functions on the
Unit Circle
More Special Triangles…Find the
missing sides.
1
?
1
?
45°
60°
?
?
Our Goal today is to learn to use the Unit Circle
to evaluate values of angles
The Unit Circle: A circle with a radius of 1 that is
placed on the xy coordinate plane with center at
the origin.
More Unit Circle
• Find the sine, cosine, and tangent of a
30° angle using the unit circle.
Sin 30° =
Cos 30° =
Tan 30° =
Always draw the triangle to the
x axis!!!
Always write the ordered pair,
and the answer is in that
point!!!!
More Unit Circle
• Find the sine, cosine, and tangent of a
60° angle using the unit circle.
Sin 60° =
Cos 60° =
Tan 60° =
Always draw the triangle to the x
axis!!!
Always write the ordered pair,
and the answer is in that point!!!!
More Unit Circle
• Find the sine, cosine, and tangent of a
45° angle using the unit circle.
Sin 45° =
Cos 45° =
Tan 45° =
Always draw the triangle to the x
axis!!!
Always write the ordered pair,
and the answer is in that point!!!!
More Unit Circle
• Find the sine, cosine, and tangent of a 210°
angle using the unit circle.
Sin 210° =
Cos 210° =
Tan 210° =
Always draw the triangle to
the x axis!!!
Always write the ordered
pair, and the answer is in
that point!!!!
More Unit Circle
• Find the sine, cosine, and tangent of a 150°
angle using the unit circle.
Sin 150° =
Cos 150° =
Tan 150° =
Always draw the triangle to
the x axis!!
Always write the ordered
pair, and the answer is in that
point!!!!
More Unit Circle
• Find the sine, cosine, and tangent of a
600° angle using the unit circle.
Sin 600° =
Cos 600° =
Tan 600° =
Always draw the triangle to the x
axis!!
Always write the ordered pair,
and the answer is in that point!!!!
More Unit Circle
• Find the sine, cosine, and tangent of a 225°
angle using the unit circle.
Sin 225° =
Cos 225° =
Tan 225° =
Always draw the triangle to
the x axis!!
Always write the ordered
pair, and the answer is in
that point!!!!
More Unit Circle
• Find the sine, cosine, and tangent of θ using
the unit circle.
Sin θ = y/1 = y
Cos θ = x/1 = x
Tan θ = y/x
These are always the ratios for an angle on the unit
circle….but remember that the radius must be 1!!!
Signs in Each Quadrant.
•
•
•
•
All
Student
Take
Calculus
(-, +)
(+, +)
(-, -)
(+, -)
Find each value using the Unit Circle.
• Cos 210°
• Sin 300°
• Cos 135 °
• Tan 480°
Build the Unit Circle
What about Reciprocal Functions?
Csc θ = 1/y
(reciprocal of Sin θ)
Sec θ = 1/x
(reciprocal of Cos θ)
Cot θ = x/y
(reciprocal of Tan θ)
Find each value using the Unit Circle.
• Sec -135°
• Csc 660°
• Cot 240 °
• Sec -225°
What about Quadrantal Angles?
•
•
•
•
•
•
Sin 90°
Cos 90°
Tan 90 °
Csc 90 °
Sec 90 °
Cot 90 °
Find each value using the Unit Circle.
• csc 270°
• Sin -225°
• Cot 495 °
• Sec -240°
Day 2
Values not on the unit circle.
Finding trig values when it is NOT
a unit circle. (Radius is not one)
Trig Ratios
Sin θ = y Csc θ =
r
Cos θ = x
r
y
Tan θ =
x
r
y
r
Sec θ =
x
x
Cot θ = y
Find the values of the six trig functions for angle θ in
standard position if a point with coordinates (5, -12)
lies on its terminal side.
Sin θ =
Csc θ =
Cos θ =
=
Sec θ
Tan θ =
Cot θ =
Always draw the triangle to the x axis!!!
Find the values of the six trig functions for angle θ in
standard position if a point with coordinates (-3, -4) lies
on its terminal side.
Sinθ=
Cosθ=
Tanθ=
Always draw the triangle to the x axis!!!
Csc θ=
Sec θ =
Cot θ=
Find the values of the six trig functions for angle θ in
standard position if a point with coordinates (-4, 2) lies
on its terminal side.
Sinθ=
Cosθ=
Tanθ=
Always draw the triangle to the x axis!!!
Csc θ=
Sec θ =
Cot θ=
Suppose θ is an angle in standard position whose terminal
side lies in Quadrant III. If sin θ = -4/5, find the values of
the remaining five trig functions.
Sinθ=
Cscθ=
Cosθ=
Tanθ=
Secθ=
Cotθ =
Suppose θ is an angle in standard position whose terminal
side lies in Quadrant IV. If sec θ = √3, find the values of the
remaining five trig functions.
Sinθ=
Csc θ=
Cosθ=
Secθ=
Tanθ=
Cotθ=