Download 5.2 Day 1 Trigonometric Functions: Unit Circle Approach

5.2
Day 1
Trigonometric Functions:
Unit Circle Approach
Triangle Sum
Theorem:
The sum of the measures of the
interior angles of a triangle is 180°.
Find the value of the missing angle.
Reference Angles and Opposite Sides and Adjacent Sides, Oh My!
Reference Angle – An acute angle of a right
triangle.
Given that angle A is
the reference angle,
what are the opposite
and adjacent legs?
What if angle C is the
reference angle?
The Pythagorean Theorem:
Given a right
triangle:
Right Triangle Definitions
Of Trigonometric Functions:
EXAMPLE 1
Evaluate trigonometric functions
Evaluate the six trigonometric functions of the angle θ.
Special Right Triangles:
EXAMPLE 3
Solve for the missing side lengths.
B = 45°, c = 5
The unit circle:
The circle with radius = 1.
In Trigonometry, the unit
circle is placed in the
coordinate plane with its
center at (0, 0).
Trigonometric Functions and the Unit Circle
The values of
sin  and cos 
are simply the y-coordinate and
x-coordinate, respectively, of the
point where the terminal side of
intersects the unit circle.
The Unit Circle and Special Right Triangles:
45  45  90
30  60  90
Find the exact value of each expression. No calculators!!
sin 30 cos 45
csc

3
 cot

4
tan

3
 cos

3