PRE-CALC

sinθ

1/cscθ

y/r

opp/hyp

cscθ

1/sinθ

r/y

hyp/opp

cosθ

1/secθ

x/r

adj/hyp

cos(-θ)

secθ

1/cosθ

r/x

hyp/adj

sec(-θ)

tanθ

1/cotθ

y/x

sinθ/cosθ

opp/adj

cotθ

1/tanθ

x/y

adj/opp

cosθ/sinθ

sin²θ

1-cos²θ

csc²θ

1+cot²θ

cos²θ

1-sin²θ

sec²θ

1+tan²θ

tan²θ

sec²θ-1

cot²θ

csc²θ-1

sin(2θ)

2sinθcosθ

cos(2θ)

cos²θ-sin²θ

1-2sin²θ

2cos²θ-1

tan(2θ)

2tanθ/1-tan²θ

sin(θ/2)

±√1-cosθ/2

cos(θ/2)

±√1+cosθ/2

tan(θ/2)

±√(1-cosθ/1+cosθ)

sinθ/1+cosθ

1-cosθ/sinθ

sin(-θ)

-sinθ

csc(-θ)

-cscθ

cos(-θ)

cosθ

sec(-θ)

secθ

tan(-θ)

-tanθ

cot(-θ)

-cotθ

sin(x+y)

sinxcosy + cosxsiny

sin(x-y)

sinxcosy - cosxsiny

cos(x+y)

cosxcosy - sinxsiny

cos(x-y)

cosxcosy + sinxsiny

tan(x+y)

tanx + tany/1 - tanxtany

tan(x-y)

tanx - tany/1 + tanxtany

sin45⁰

cos45º

tan45º

√2/2

√2/2

1

sin30º

cos30º

tan30º

1/2

√3/2

√3/3

sin60º

cos60º

tan60º

√3/2

1/2

√3

sinπ/4

cosπ/4

tanπ/4

√2/2

√2/2

1

sinπ/6

cosπ/6

tanπ/6

1/2

√3/2

√3/3

sinπ/3

cosπ/3

tanπ/3

√3/2

1/2

√3

Pythagorean Triples

3,4,5

5,12,13

6,8,10

7,24,25

8,15,17

9,40,41

sin²θ+cos²θ

=1