Radians to Degrees, Degrees to Radians, and Reference Angles
What is a degree?
What is a radian?
Conversions Between Degrees and Radians
Degrees to Radians:
Radians to Degrees:
1
What is a reference angle?
-an angle that measures from the ray to the x-axis
-it is ALWAYS POSITIVE
Sketch the angle and find its reference angle.
a) 210o
b) 85o
c) - π
d) -360o
e) 100o
f) 280o
3
Special Right Triangles
Recall the 45o, 45o, 90o triangle and it's proportions:
Recall the 30o, 60o, 90o triangle and it's proportions:
2
Given the angle, determine the reference angle, θ, sketch the
reference triangle, and label all angles and sides of the
triangle.
ex)
3π
4
ex) - 120o
Imagine that we are working "within" the unit circle. The
hypotenuse intersects with the unit circle. Label the
coordinates of the intersection.
Recall the 6 Trig Functions:
Sin θ =
Csc θ =
Cos θ =
Sec θ =
Tan θ =
Cot θ =
3
Quotient Identities:
tan θ =
cot θ =
cos 30o
sin -210o
tan 11π
6
4
sec 150o
csc 420o
cot 3π
2
hw: WKST - USING A PENCIL!!!!!!!
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sketch the angle with a smooth curve
determine the reference angle
draw the reference triangle
label all sides
label the coordinate
find the trig function using correct algebra
(JUST LIKE THE LAST FEW EXAMPLES)
5