Download Unit 12 – Trigonometry Study Sheet Right Triangle Trig

Unit 12 – Trigonometry Study Sheet
Right Triangle Trig:
O
A
O
S
C
T
H
H
A
Angle of Elevation: line of sight is titled upward
angle of
elevation
forms a right
angle
horizontal line
Angle of Depression: line of sight is titled downward
horizontal line
angle of
depression
forms a right
angle
horizontal line
Remember: The measure of the angle of depression is equal to the measure of the angle of elevation.
Reciprocal Trig Functions
sin θ 
opposite
hypotenuse
cos θ 
adjacent
hypotenuse
tan θ 
opposite
adjacent
csc θ 
hypotenuse
opposite
sec θ 
hypotenuse
adjacent
cot θ 
adjacent
opposite
To find a coterminal angle
 Add or subtract 360° from the given angle
Converting between radians and degrees:
The measure of any angle can be expressed in degrees or in radians. We can
do this by forming the following proportion:
OR
To convert from DEGREES to
RADIANS:
Multiply by

180
.
To convert from RADIANS to
DEGREES:
180
Multiply by
.

Clock Problems – Find the number of radians in the angle formed by hands
of a clock.
Special Right Triangles:
30 – 60 – 90
30°
45 – 45 – 90
45°
2
1
60°
45°
1
1
Reference Angles:
S
A
T C
reference
angle
reference
angle
A reference angle is the angle formed
by the terminal side of the angle in
standard position and the x-axis.
θ = reference
angle
reference
angle
“ASTC” with Reciprocal Trig Functions
Sign Chart (ASTC):
Sin and Csc are positive (QII)
All functions are positive (QI)
Tan and Cot are positive (QIII)
Cos and Sec are positive (QIV)
Reciprocal Identities
csc  
1
sin
sec  
1
cos
cot  
Tangent and Cotangent Identities
tan  
sin
cos
cot  
Pythagorean Identity
Cofunction Identity
Sine and cosine are cofunctions.
**Remember the relationship between cofunction and complementary**
 Cofunctions are equal in value only when their angles add to 90o
cos
sin
1
tan 
The Unit Circle:
(0, 1)
(1, 0)
(-1, 0)
(0, -1)