Trigonometry ( bridging the gap ) - Exact values Flashcards
CAST
Relationship of 2nd quadrant
Sin
sin ( 180 - x ) = sin x
sin (180 + x ) = - sin x
sin ( 360 - x) = - sin x
CAST
Relationship of 4th quadrant
cos
cos ( 180 - x ) = - cos x
cos (180 + x ) = - cos x
cos ( 360 - x) = cos x
CAST
Relationship of 3rd quadrant
tan
tan ( 180 - x ) = - tan x
tan (180 + x ) = tan x
tan ( 360 - x) = - tan x
right angled triangle are considered ..
to complementary
q
sinx = - = cos ( 90 - x ) and
r
q cosx = - = sin ( 90 - x )
r
Exact values for sin 30 ..
1
-
2
Exact values for sin 45…
1
-
√ 2
Exact values for sin 60 …
√3
-
2
Exact values for cos 30 ..
√3
-
2
Exact values for cos 45…
1
-
√ 2
Exact values for cos 60 …
1
-
2
Exact values for tan 30 ..
1
-
√ 3
Exact values for tan 45…
1
Exact values for tan 60 …
√ 3
Exact values for sin 90 …
1
Exact values for cos 90 …
0
Exact values for tan 90 …
undefined
Exact values for cos 0 …
1
Exact values for tan 0 …
0
Exact values for sin 0 …
0
degrees into radians
_____ ÷180
then X π
radians into degree
____÷ π
then x 180
y = 2sin(4x + 45) + 1
find period?
Period = 360 ÷4 = 90
y = 2sin(4x + 45) + 1
find maximum?
Max. Value =2+1= 3
y = 2sin(4x + 45) + 1
find minimum?
Mini. Value = -2+1 -1
