Studied by 20 peoplemultiply by 180/π
Convert radians to degrees
1
cos (2π) / 0
0
sin (2π) / 0
0
tan (2π) / 0
√3/2
cos (π/6)
1/2
sin (π/6)
√3/3
tan (π/6)
√2/2
cos (π/4)
√2/2
sin (π/4)
1
tan (π/4)
1/2
cos (π/3)
√3/2
sin (π/3)
√3
tan (π/3)
0
cos (π/2)
1
sin (π/2)
undefined
tan (π/2)
√3, √2, √1 all divided by 2
If we go from the bottom angle (π/6) to the top angle (π/3), the values of cos x will be...
√1, √2, √3 all divided by 2
If we go from the bottom angle (π/6) to the top angle (π/3), the values of sin x will be...
values of cos will be negatives, while values of sin will be positive
Rules for values in the II quadrant (notable angles between 2π/3 & 5π/3) are...
values of cos and sin will both be negative
Rules for values in the III quadrant (notable angles between 7π/6 & 4π/3) are...
values of cos will be positive, while values of sin will be negative
Rules for values in the IV quadrant (notable angles between 5π/3 & 11π/6) are...
sin x/cos x, or 1/cot x
tan x=
1/cos x or Hypotenuse/Adjacent
sec x =
1/sin x or Hypotenuse/Opposite
csc x =
cos x/sin x, or 1/tan x
cot x =
f'(u)u'
Chain Rule (Trigonometry) d/dx [f(u)]
The denominator - 1
Rules for angles in the second quadrant
2π/3 (120 degrees)
What's the angle for π/3 in the second quadrant?
3π/4 (135 degrees)
What's the angle for π/4 in the second quadrant?
5π/6 (150 degrees)
What's the angle for π/6 in the second quadrant?
2π/3 -> 120 3π/4 -> 135 5π/6 -> 150
Angles in the second quadrant
The denominator + 1
Rule for angles in the third quadrant
7π/6 (210 degrees)
What's the angle for π/6 in the third quadrant?
5π/4 (225 degrees)
What's the angle for π/4 in the third quadrant?
4π/3 (240 degrees)
What's the angle for π/3 in the third quadrant?
The denominator x2 - 1
Rule for angles in the fourth quadrant
5π/3 (300 degrees)
What's the angle for π/3 in the fourth quadrant?
7π/4 (315 degrees)
What's the angle for π/4 in the fourth quadrant?
11π/6 (330 degrees)
What's the angle for π/6 in the fourth quadrant?
always be negative
Derivatives of functions with "co" in their name will...
just be each other
Derivatives of cos and sin will....
always be squared, and either secant or cosecant
Derivatives of tangent and cotangent will...
just be themselves multiplied by either tan or cotangent
Derivatives of secant and cosecant will...
-sin x
d/dx [cos x]
cos x
d/dx [sin x]
sec^2 x
d/dx [tan x]
-csc^2 x
d/dx [cot x]
-csc x cot x
d/dx [csc x]
sec x tan x
d/dx [sec x]
To find the angle which gives us an specific value
Inverse Trig Functions asks us...
arctan u, arcos u, & arc sin u
The Inverse Trig Functions are
u' / 1+u^2
d/dx [arctan u]
-u'/√(1-u^2)
d/dx [arccos u]
u'/√(1-u^2)
d/dx [arcsin u]
1
sin^2 x + cos^2 x =
tan^2 x + 1
sec^2 x =
cot^2 x + 1
csc^2 x =
1st and 2d quadrants, 0/2π - π
Range of arc cos x
4th and 1st quadrant, 3π/2 - π/2
Range of arcsin x and arctan x
Note
Flashcard