## Pre-Calculus Tutorial

*5.1 Trig Identities - Reciprocal and Quotient Identities*

#### Intro

These identities deal with the reciprocal(s) of the problem given.

#### Sample Problem

If SIN(x) = 5/6, find CSC(x).

#### Solution

**CSC** and **SIN** are reciprocals of one another, and therefor, to find the answer, you just have to flip the values given for **SIN(x)**

**SIN**, **COS**, and **TAN**, all have reciprocals, I will include them below.

**SIN (Sine) CSC (Cosecant)
COS (Cosine) SEC (Secant)
TAN (Tangent) COT (Cotangent)**

How you can remember these effectively is no two start on the same letter. For example, the reciprocal of **Sine**, which starts with an *“S”*, is **Cosecant**, starting with a *“C”*. The same goes for **Cosine** *“C”* and **Secant** *“S”*, and **Tangent*** “T”* and **Cotangent** *“C”*. All six line up, and remain in the same spot, no matter the equation. So **Cosecant** will __always__ be the reciprocal of **Sine**, no matter if the equation changes or not.

So, going back to the equation:

**If SIN(x) = 5/6, Find CSC(x)**

With the information above, we know that **CSC**, or **Cosecant**, is the reciprocal of **SIN**, or **Sine**, and therefor, we just need to flip the value given to **SIN**: **5/6**

**So, CSC(x) = 6/5.**

Leave **6/5** like it is, don’t bother making it into a decimal or changing it in any way.

# About The Author

Science, English, And Art Helper (With A Little Ex |

Hello, I'm Kristen Moore, an 18 year old senior in Highschool who has had an array of classes including, but not limited to, AP Biology, AP Chemestry, AP English I-IV AP Algebra I (Not my strongest subject), Algebra II (Not my strong subject), AP Geometry, AP World Geography, AP World History, AP US... |

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