trig derivatives + unit circle coords

what are the coordinates at 2π?

(1,0)

what is the sin(2π)?

0

what is the cos(2π)?

1

what are the coordinates at π/6?

(√3/2, 1/2)

what is the sin(π/6)?

1/2

what is the cos(π/6)?

√3/2

what are the coordinates at π/4?

(√2/2, √2/2)

what is the cos(π/4)?

√2/2

what is the sin(π/4)?

√2/2

what are the coordinates at π/3?

(1/2, √3/2)

what is the cos(π/3)?

1/2

what is the sin(π/3)?

√3/2

what are the coordinates at π/2?

(0,1)

what is the cos(π/2)?

0

what is the sin(π/2)?

1

what is the derivative of sin(x)?

cos(x)

what is the derivative of cos(x)?

-sin(x)

what is the derivative of tan(x)?

sec²(x)

what is the reciprocal of sec²x?

1/cos²(x)

what are the coordinates at 2π/3?

(-1/2, √3/2)

what is the cos(2π/3)?

-1/2

what is the sin(2π/3)?

√3/2

what are the coordinates at 3π/4?

(-√2/2, √2/2)

what is the cos(3π/4)?

-√2/2

what is the sin(3π/4)?

√2/2

what are the coordinates at 5π/6?

(-√3/2, 1/2)

what is the cos(5π/6)?

-√3/2

what is the sin(5π/6)?

1/2

what is the derivative of csc(x)?

-csc(x) * cot(x)

what is the reciprocal of csc(x)?

sin(x)

what is the derivative of sec(x)?

sec(x) * tan(x)

what is the reciprocal of sec(x)?

cos(x)

what is the derivative of cot(x)?

-csc²(x)

what is the reciprocal of cot(x)?

tan(x)

what are the coordinates at π?

(-1,0)

what is the cos(π)?

-1

what is the sin(π)?

0

what are the coordinates at 7π/6?

(-√3/2, -1/2)

what is the cos(7π/6)?

-√3/2

what is the sin(7π/6)?

-1/2

what are the coordinates at 5π/4?

(-√2/2, -√2/2)

what is the cos(5π/4)?

-√2/2

what is the sin(5π/4)?

-√2/2

what are the coordinates at 4π/3?

(-1/2, -√3/2)

what is the cos(4π/3)?

-1/2

what is the sin(4π/3)?

-√3/2

what are the coordinates at 3π/2?

(0,-1)

what is the cos(3π/2)?

0

what is the sin(3π/2)?

-1

what are the coordinates at 5π/3?

(1/2, -√3/2)

what is the cos(5π/3)?

1/2

what is the sin(5π/3)?

-√3/2

what are the coordinates at 7π/4?

(√2/2, -√2/2)

what is the cos(7π/4)?

√2/2

what is the sin(7π/4)?

-√2/2

what are the coordinates at 11π/6?

(√3/2, -1/2)

what is the cos(11π/6)?

√3/2

what is the sin(11π/6)?

-1/2