1.fold the plate into 4 quarters and draw two perpendicular lines on the creases. 2.label the...
TRANSCRIPT
1. Fold the plate into 4 quarters and draw two perpendicular lines on the creases.
2. Label the degrees in one color, radians in another color, and the coordinates in a third color.
0º
90º
180º
270º
0
/2
3/2
(1,0)
(0,1)
(-1,0)
(0,-1) 3. Fold the plate into eights, draw light dotted lines on the new creases and repeat the procedure in step 2.
45º135º
225º 315º
/43/4
5/4 7/4
/222,2 /222,2
/222,-2 /222,-2
4. Label the quadrants and include the acronym A S T C
0º
90º
180º
270º
0
/2
3/2
(1,0)
(0,1)
(-1,0)
(0,-1)
45º135º
225º 315º
/43/4
5/4 7/4
/222,2 /222,2
/222,-2 /222,-2
I A (+ +)
II S (- +)
III T (- -)
IV C (+ -)
5. Measure halfway from the origin to the edge of the arrows. Go to the rim and find all the multiples of 30º.
6. Label the angle measure in degrees, radians, and the coordinates.
30º
60º120º
150º
210º
240º 300º
330º
/6
/32/3
5/6
7/6
4/3 5/3
11/6
2,1/23
/232,1 /232,1-
1/23 ,2
2,-1/23
/232,-1- /232,-1
2,-1/23
7. Turn the plate over, fold back into quarters and cut out a small notch. Label the notches in rectangular and polar coordinates.
(x,y)(-x,y)
(-x,-y) (x,-y)
(r,)(r,-)
(r,+) (r,2-)
8. Draw a hexagon, connect the opposite vertices and label the six vertices with the 6 trigonometric relations
sin x cos x
cot x
csc xsec x
tan x
9. Shade the three triangles as shown and put a 1 with a circle in the center.
1
Quotient Identities
sin x cos x
cot x
csc xsec x
tan x1
x
xx
cos
sintan
x
xx
cot
cossin
x
xx
csc
cotcos
x
xx
sec
csccot
x
xx
tan
seccsc
x
xx
sin
tansec
Product Identities
sin x cos x
cot x
csc xsec x
tan x1
xxx costansin
xxx cotsincos
xxx seccoscot
xxx seccotcsc
xxx tancscsec
xxx secsintan
cot x
csc x
sec x
tan x
Pythagorean Identities
cos x
1
sin x
sec x
sin2x + cos2x = 1
cos xsin x
sin2x + cos2x = 1
cos xsin x
sin2x + cos2x = 1
cos xsin x
sin2x + cos2x = 1
cos xsin x
tan2x + 1= sec2xtan x
sec x
1tan2x + 1= sec2xtan x
sec x
1tan2x + 1= sec2xtan x
sec x
1tan2x + 1= sec2xtan x
sec x
11+ cot2x = csc2x cot x
csc x
11+ cot2x = csc2x cot x
csc x
11+ cot2x = csc2x cot x
csc x
11+ cot2x = csc2x cot x
csc x
1
sin2x + cos2x = 1
cos xsin x
tan2x + 1= sec2xtan x
sec x
11+ cot2x = csc2x cot x
csc x
1
(x,y)(-x,y)
(-x,-y) (x,-y)
(r,)(r,-)
(r,+) (r,2-)
sin x cos x
tan x
csc xsec x
cot x1
xx
csc
1sin
xx
csc
1sin
xx
csc
1sin
xx
csc
1sin
xx
sec
1cos
xx
sec
1cos
xx
sec
1cos
xx
sec
1cos
xx
cot
1tan
xx
cot
1tan
xx
cot
1tan
xx
cot
1tan
xx
csc
1sin
xx
sec
1cos
xx
cot
1tan
Reciprocal Identities