Trigonometry is the branch of mathematics dealing with the relationship of sides and angles of triangles.

Subjects > Mathematics > Trigonometry 1

Before moving direct into the problems of Trigonometry 1, let's see what we need to know about Trigonometry.

Consider the following diagram.

let use `opp` = opposite, `hyp` = hypotenuse and `adj` = adjacent

From the diagram above,

`sin theta = (opp)/(hyp) = y/r`

`cos theta = (adj)/(hyp) = x/r`

`tan theta = (opp)/(adj) = y/x`

`csc theta = (hyp)/(opp) = r/y`

`sec theta = (hyp)/(adj) = r/x`

`cot theta = (adj)/(opp) = x/y`

`csc theta = 1/(sin theta)`

`sec theta = 1/(cos theta)`

`cot theta = 1/(tan theta)`

Degrees | `0^0` | `30^0` | `45^0` | `60^0` | `90^0` | `180^0` | `270^0` |
---|---|---|---|---|---|---|---|

Radians | 0 | `(pi)/6` | `(pi)/4` | `(pi)/3` | `(pi)/2` | `pi` | `(3pi)/2` |

`sin theta` | `0` | `1/2` | `(sqrt(2))/2` | `(sqrt(3))/2` | `1` | `0` | `-1` |

`cos theta` | `1` | `(sqrt(3))/2` | `(sqrt(2))/2` | `1/2` | `0` | `-1` | `0` |

`tan theta` | `0` | `(sqrt(3))/3` | `1` | `sqrt(3)` | undefined | `0` | undefined |

Unit circle is a circle with radius of 1, and it is used to show certain common angles.

`1 + tan^2 x = sec^2 x`

`1 + cot^2 x = csc^2 x`

`tan x = pm sqrt(sec^2 x - 1)`

`cos x = pm sqrt(1 - sin^2 x)`

`cot x = pm sqrt(csc^2 x - 1)`

`csc (-x) = -csc x`

`tan (-x) = -tan x`

`cot (-x) = -cot x`

`sec (-x) = sec x`

`sin (A - B) = sin Acos B - cos Asin B`

`cos (A + B) = cos Acos B - sin Asin B`

`cos (A - B) = cos Acos B + sin Asin B`

`tan (A + B) = (tan A + tan B)/(1 - tan Atan B)`

`tan (A - B) = (tan A - tan B)/(1 - tan Atan B)`

`cos ((pi)/2 - x) = sin x`

`tan ((pi)/2 - x) = cot x`

`cot ((pi)/2 - x) = tan x`

`sec ((pi)/2 - x) = csc x`

`csc ((pi)/2 - x) = sec x`

`cos A/2 = pm sqrt((1 + cos A)/2)`

`tan A/2 = (1 - cos A)/(sin A)`

`tan A/2 = (sin A)/(1 + cos A)`

You can learn more about Trigonometry 2 here.

Now, let's move in. **Solved Trigonometry questions**

**Recommended Lessons**

Before moving direct into the problems of Trigonometry 1, let's see what we need to know about Trigonometry.

Consider the following diagram.

let use `opp` = opposite, `hyp` = hypotenuse and `adj` = adjacent

From the diagram above,

`sin theta = (opp)/(hyp) = y/r`

`cos theta = (adj)/(hyp) = x/r`

`tan theta = (opp)/(adj) = y/x`

`csc theta = (hyp)/(opp) = r/y`

`sec theta = (hyp)/(adj) = r/x`

`cot theta = (adj)/(opp) = x/y`

`csc theta = 1/(sin theta)`

`sec theta = 1/(cos theta)`

`cot theta = 1/(tan theta)`

Degrees | `0^0` | `30^0` | `45^0` | `60^0` | `90^0` | `180^0` | `270^0` |
---|---|---|---|---|---|---|---|

Radians | 0 | `(pi)/6` | `(pi)/4` | `(pi)/3` | `(pi)/2` | `pi` | `(3pi)/2` |

`sin theta` | `0` | `1/2` | `(sqrt(2))/2` | `(sqrt(3))/2` | `1` | `0` | `-1` |

`cos theta` | `1` | `(sqrt(3))/2` | `(sqrt(2))/2` | `1/2` | `0` | `-1` | `0` |

`tan theta` | `0` | `(sqrt(3))/3` | `1` | `sqrt(3)` | undefined | `0` | undefined |

Unit circle is a circle with radius of 1, and it is used to show certain common angles.

`1 + tan^2 x = sec^2 x`

`1 + cot^2 x = csc^2 x`

`tan x = pm sqrt(sec^2 x - 1)`

`cos x = pm sqrt(1 - sin^2 x)`

`cot x = pm sqrt(csc^2 x - 1)`

`csc (-x) = -csc x`

`tan (-x) = -tan x`

`cot (-x) = -cot x`

`sec (-x) = sec x`

`sin (A - B) = sin Acos B - cos Asin B`

`cos (A + B) = cos Acos B - sin Asin B`

`cos (A - B) = cos Acos B + sin Asin B`

`tan (A + B) = (tan A + tan B)/(1 - tan Atan B)`

`tan (A - B) = (tan A - tan B)/(1 - tan Atan B)`

`cos ((pi)/2 - x) = sin x`

`tan ((pi)/2 - x) = cot x`

`cot ((pi)/2 - x) = tan x`

`sec ((pi)/2 - x) = csc x`

`csc ((pi)/2 - x) = sec x`

`cos A/2 = pm sqrt((1 + cos A)/2)`

`tan A/2 = (1 - cos A)/(sin A)`

`tan A/2 = (sin A)/(1 + cos A)`

You can learn more about Trigonometry 2 here.

Now, let's move in. **Solved Trigonometry questions**

**Recommended Lessons**