+
|\
| \
| \
| \
| \
| \
|ﬢ θ \
+-------+
sine: sinθ = opposite / hypotenuse
cosine: cosθ = adjacent / hypotenuse
tangent: tanθ = opposite / adjacent
cosec: cosecθ = 1/sinθ
sec: secθ = 1/cosθ
cotangent: cotθ = 1/tanθ
arcsin = sin⁻¹
| Radian | Degree | sin | cos | tan |
|--------+--------+------+------+------|
| 0 | 0 | 0 | 1 | 0 |
| π/6 | 30 | 1/2 | √3/2 | 1/√3 |
| π/4 | 45 | 1/√2 | 1/√2 | 1 |
| π/3 | 60 | √3/2 | 1/2 | √3 |
| π/2 | 90 | 1 | 0 | ∞ |
From Wikipedia:
| | sin | cos | tan | cosec | sec | cot |
|--------+-------------+-------------+-------------+---------------+-------------+-------------|
| | | | | | | |
| | | | tan²θ | 1 | sec²θ - 1 | 1 |
| sin | sin²θ | 1 - cos²θ | ─────────── | ─────────── | ─────────── | ─────────── |
| | | | 1 + tan²θ | sin²θ | sec²θ | 1 + cot²θ |
|--------+-------------+-------------+-------------+---------------+-------------+-------------|
| | | | | | | |
| | | | 1 | cosec²θ - 1 | 1 | cot²θ |
| cos | 1 - sin²θ | cos²θ | ─────────── | ─────────── | ─────────── | ─────────── |
| | | | 1 + tan²θ | cosec²θ | sec²θ | 1 + cot²θ |
| | | | | | | |
|--------+-------------+-------------+-------------+---------------+-------------+-------------|
| | | | | | | |
| | sin²θ | 1 - cos²θ | | 1 | | 1 |
| tan | ─────────── | ─────────── | tan²θ | ───────────── | sec²θ - 1 | ─────────── |
| | 1 - sin²θ | cos²θ | | cosec²θ - 1 | | cot²θ |
| | | | | | | |
|--------+-------------+-------------+-------------+---------------+-------------+-------------|
| | | | | | | |
| | 1 | 1 | | 1 + tan²θ | sec²θ | |
| cosec | ─────── | ─────────── | tan²θ | ─────────── | ─────────- | 1 + cot²θ |
| | sin²θ | 1 - cos²θ | | tan²θ | sec²θ - 1 | |
| | | | | | | |
|--------+-------------+-------------+-------------+---------------+-------------+-------------|
| | | | | | | |
| | 1 | 1 | | cosec²θ | | 1 + cot²θ |
| sec | ────────── | ──────── | 1 + tan²θ | ─────────── | sec²θ | ────────── |
| | 1 - sin²θ | cos²θ | | cosec²θ - 1 | | cot²θ |
| | | | | | | |
|--------+-------------+-------------+-------------+---------------+-------------+-------------|
| | | | | | | |
| | 1 - sin²θ | cos²θ | 1 | | 1 | |
| cot | ────────── | ────────── | ────── | cosec²θ - 1 | ─────── | cot²θ |
| | sin²θ | 1 - cos²θ | tanθ | | sec²θ | |
| | | | | | | |
| Function | -θ | π/2 - θ | π - θ | 3π/4 - θ |
|----------+---------+---------+--------+----------|
| sinθ | -sinθ | cosθ | sinθ | -cosθ |
|----------+---------+---------+--------+----------|
| cosθ | cosθ | sinθ | -cosθ | -sinθ |
|----------+---------+---------+--------+----------|
| tanθ | -tanθ | cotθ | -tanθ | cotθ |
|----------+---------+---------+--------+----------|
| cosecθ | -cosecθ | secθ | cosecθ | -secθ |
|----------+---------+---------+--------+----------|
| secθ | secθ | cosecθ | -secθ | -cosecθ |
|----------+---------+---------+--------+----------|
| cotθ | -cotθ | tanθ | -cotθ | tanθ |
Functions with period 2π:
| Function | θ ± (π/2) | +π |
|----------+-----------+---------|
| sin | ± cosθ | -sinθ |
| cos | ∓ sinθ | -cosθ |
| cosec | ± secθ | -cosecθ |
| sec | ∓ cosecθ | -secθ |
Functions with period π:
| Function | θ ± (π/4) | +(π/2) |
|----------+-----------+--------|
| | tanθ ± 1 | |
| tan | ───────── | ─cotθ |
| | 1 ∓ tanθ | |
|----------+-----------+--------|
| | cotθ ∓ 1 | |
| cot | ───────── | ─tanθ |
| | 1 ± cotθ | |
| sin(A±B) | sinA.cosB ± cosA.sinB |
|-----------------+-----------------------------|
| cos(A±B) | cosA.cosB ∓ sinA.sinB |
|-----------------+-----------------------------|
| | tanA ± tanB |
| tan(A±B) | ──────────────── |
| | 1 ∓ tanA.tanB |
|-----------------+-----------------------------|
| | secA.secB.cosecA.cosecB |
| cosec(A±B) | ────────────────────────── |
| | secA.cosecB ± cosecA.secB |
|-----------------+-----------------------------|
| | secA.secB.cosecA.cosecB |
| sec(A±B) | ────────────────────────── |
| | cosecA.cosecB ∓ secA.secB |
|-----------------+-----------------------------|
| | cotA.cotB ∓ 1 |
| cot(A±B) | ───────────── |
| | cotB ∓ cotA |
|-----------------+-----------------------------|
| | ⎛ ⎞ |
| sin⁻¹x ± sin⁻¹y | sin⁻¹⎜x√(1-y²) ± y√(1-x²) ⎟ |
| | ⎝ ⎠ |
|-----------------+-----------------------------|
| | ⎛ ⎞ |
| cos⁻¹x ± cos⁻¹y | cos⁻¹⎜xy ∓ √[(1-x²)(1-y²)]⎟ |
| | ⎝ ⎠ |
|-----------------+-----------------------------|
| | ⎛ x ± y ⎞ |
| tan⁻¹x ± tan⁻¹y | tan⁻¹⎜─────────⎟ |
| | ⎝ 1 ∓ xy ⎠ |
|-----------------+-----------------------------|
| | ⎛ xy ∓ 1 ⎞ |
| cot⁻¹x ± cot⁻¹y | cot⁻¹⎜─────────⎟ |
| | ⎝ y ± x ⎠ |
| | | | 2.tanθ | |
| sin2θ | 2.sinθ.cosθ | (sinθ + cosθ)² ─ 1 | ──────────── | |
| | | | 1 + tan²θ | |
|---------+---------------+--------------------+--------------+--------------|
| | | | | 1 - tan²θ |
| cos2θ | cos²θ - sin²θ | 2.cos²θ - 1 | 1 - 2.sin²θ | ──────────── |
| | | | | 1 + tan²θ |
|---------+---------------+--------------------+--------------+--------------|
| | 2.tanθ | | | |
| tan2θ | ───────────── | | | |
| | 1 - tan²θ | | | |
|---------+---------------+--------------------+--------------+--------------|
| | secθ.cosecθ | 1 + tan²θ | | |
| cosec2θ | ───────────── | ───────── | | |
| | 2 | 2.tanθ | | |
|---------+---------------+--------------------+--------------+--------------|
| | sec²θ | 1 + tan²θ | | |
| sec2θ | ───────────── | ───────── | | |
| | 2 - sec²θ | 1 - tan²θ | | |
|---------+---------------+--------------------+--------------+--------------|
| | cot²θ - 1 | 1 - tan²θ | | |
| cot2θ | ───────────── | ─────────── | | |
| | 2.cotθ | 2.tanθ | | |
| | | ⎛ π ⎞ ⎛ π ⎞ |
| sin3θ | 3.sinθ - 4sin³θ | 4.sinθ.sin⎜─── - θ⎟.sin⎜─── + θ⎟ |
| | | ⎝ 3 ⎠ ⎝ 3 ⎠ |
|---------+-----------------+----------------------------------|
| | | ⎛ π ⎞ ⎛ π ⎞ |
| cos3θ | 4cos³θ - 3.cosθ | 4.cosθ.cos⎜─── - θ⎟.cos⎜─── + θ⎟ |
| | | ⎝ 3 ⎠ ⎝ 3 ⎠ |
|---------+-----------------+----------------------------------|
| | 3.tanθ - tan³θ | ⎛ π ⎞ ⎛ π ⎞ |
| tan3θ | ─────────────── | tanθ.tan⎜─── - θ⎟.tan⎜─── + θ⎟ |
| | 1 - 3.tan²θ | ⎝ 3 ⎠ ⎝ 3 ⎠ |
|---------+-----------------+----------------------------------|
| | cosec³θ | |
| cosec3θ | ───────────── | |
| | 3.cosec²θ - 4 | |
|---------+-----------------+----------------------------------|
| | sec³θ | |
| sec3θ | ───────────── | |
| | 4 - 3.sec²θ | |
|---------+-----------------+----------------------------------|
| | 3.cotθ - cot³θ | |
| cot3θ | ────────────── | |
| | 1 - 3.cot²θ | |
From Wikipedia:
sinθ ≈ θ