Trigonometry

multiply 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