Special Values
Precalculus HS Mathematics Unit: 03 Lesson: 03
Special Values W T i l W This activity will teach you how to evaluate trigonometric expressions like these, without having to use a calculator. It's as easy as Q - R - S - T !
sin 300°
cosf
sec(-f)
tan (-225°)
cot^
csc^
Q
Find the Quadrant in which the rotation angle terminates.
R
Label the Reference angle, and draw the Reference triangle.
S
Label the S p e c i a l S i d e s of the triangle ( ± 1 , ± 1 , V2 ; or ± 1, ± V s , 2; or maybe ± 1 , 0 , 1 ) .
T
Tell the Trigonometric ratios.
S a m p l e A : Evaluate sin 300° (without a calculator)
Q
Sketch the rotation angle in the correct Quadrant.
Quadrant:
R
What is the Reference angle? Draw the Reference triangle.
Reference Z :
S
Label the S i d e s with S p e c i a l values.
Sides:
T
Tell the Trigonometric ratio(s) for this angle.
sin 300° =
Sample B: Evaluate s e c ( ^ ^ ) (without a calculator)
Q
Sketch the rotation angle in the correct Quadrant.
Quadrant:
R
What is the Reference angle? Draw the Reference triangle.
Reference Z :
S
Label the S i d e s with S p e c i a l values.
Sides:
T
Tell the Trigonometric ratio(s) for this angle.
sec(-f) =
For S a m p l e B determine a// of the trigonometric ratios: sin(-^)
©2012, T E S C C C
cos(-^)
tan(-^)
cot(-^)
07/25/12
sec(-^)
csc(-^)
page 1 of 2
Precalculus HS Mathematics Unit: 03 Lesson: 03
Special Values S a m p l e C : Evaluate s i n ^ (without a calculator)
Q
Sketch the rotation angle in the correct quadrant.
N O quadrant! W h e r e is it?
R
What is the reference angle? Draw the reference triangle.
S
Label the sides with special values.
N O reference triangle! For values, pick a point on the terminal side:
T
Tell the trigonometric ratio(s) for this angle.
(
, X
) y
/•
A n g l e s w h o s e terminal sides lie on the a x e s are called quadrantal angles. Without a calculator.
r= 1
e in
e in
Radians
Degrees
sin 9
cos
0
tan
0
COt0
sec
0
CSC 0
0 90°
(0,1) 270° (-1,0)
(1,0) 450°
(0,-1)
Without a calculator, evaluate e a c h of the following trigonometric expressions for their special values. If necessary, use a separate sheet of paper. 1)tan (-225°)
2) c o s f
3) c o t ^
4) sin
5) s e c f
6) c o s 315°
8) t a n f
9) sin(-210°)
7t
7) c s c ^
©2012, T E S C C C
07/25/12
page 2 of 2
Special Values W T i l W This activity will teach you how to evaluate trigonometric expressions like these, without having to use a calculator. It's as easy as Q - R - S - T !
sin 300°
cosf
sec(-f)
tan (-225°)
cot^
csc^
Q
Find the Quadrant in which the rotation angle terminates.
R
Label the Reference angle, and draw the Reference triangle.
S
Label the S p e c i a l S i d e s of the triangle ( ± 1 , ± 1 , V2 ; or ± 1, ± V s , 2; or maybe ± 1 , 0 , 1 ) .
T
Tell the Trigonometric ratios.
S a m p l e A : Evaluate sin 300° (without a calculator)
Q
Sketch the rotation angle in the correct Quadrant.
Quadrant:
R
What is the Reference angle? Draw the Reference triangle.
Reference Z :
S
Label the S i d e s with S p e c i a l values.
Sides:
T
Tell the Trigonometric ratio(s) for this angle.
sin 300° =
Sample B: Evaluate s e c ( ^ ^ ) (without a calculator)
Q
Sketch the rotation angle in the correct Quadrant.
Quadrant:
R
What is the Reference angle? Draw the Reference triangle.
Reference Z :
S
Label the S i d e s with S p e c i a l values.
Sides:
T
Tell the Trigonometric ratio(s) for this angle.
sec(-f) =
For S a m p l e B determine a// of the trigonometric ratios: sin(-^)
©2012, T E S C C C
cos(-^)
tan(-^)
cot(-^)
07/25/12
sec(-^)
csc(-^)
page 1 of 2
Precalculus HS Mathematics Unit: 03 Lesson: 03
Special Values S a m p l e C : Evaluate s i n ^ (without a calculator)
Q
Sketch the rotation angle in the correct quadrant.
N O quadrant! W h e r e is it?
R
What is the reference angle? Draw the reference triangle.
S
Label the sides with special values.
N O reference triangle! For values, pick a point on the terminal side:
T
Tell the trigonometric ratio(s) for this angle.
(
, X
) y
/•
A n g l e s w h o s e terminal sides lie on the a x e s are called quadrantal angles. Without a calculator.
r= 1
e in
e in
Radians
Degrees
sin 9
cos
0
tan
0
COt0
sec
0
CSC 0
0 90°
(0,1) 270° (-1,0)
(1,0) 450°
(0,-1)
Without a calculator, evaluate e a c h of the following trigonometric expressions for their special values. If necessary, use a separate sheet of paper. 1)tan (-225°)
2) c o s f
3) c o t ^
4) sin
5) s e c f
6) c o s 315°
8) t a n f
9) sin(-210°)
7t
7) c s c ^
©2012, T E S C C C
07/25/12
page 2 of 2
