HPC Ch.5 Intro Activity

Trig Identities are equalities that involve trig functions and are true for all values of the defined variable.

Reciprocal Identities

Even & Odd Identities

Pythagorean Identities

Quotient Identities and much MUCH more!

Since they are true for all values, we prove them 1st, and then use them in our proofs.

 $\sin\ x\ =\ \frac{1}{\csc\ x}$  

 $\cos\ x\ =\ \frac{1}{\sec\ x}$  

 $\tan\ x\ =\ \frac{1}{\cot\ x}$  

 $\csc\ x\ =\ \frac{1}{\sin\ x}$  

 $\sec\ x\ =\ \frac{1}{\cos\ x}$  

 $\cot\ x\ =\ \frac{1}{\tan\ x}$  

sin(-x) = - sin x

cos(-x) = cos x

tan(-x) = - tan x

csc(-x) = - csc x

sec(-x) = sec x

cot (-x) = - cot x

sin² x + cos² x = 1. Notice sin² x is equivalent as (sin x)(sin x)

1 + tan² x = sec² x

1 + cot² x = csc² x

Study 3 Pythagorean Identities for 5 min.

 $\tan\ x\ =\ \frac{\sin\ x\ }{\cos\ x}$  

 $\cot\ x\ =\ \frac{\cos\ x}{\sin\ x}$  

Sometimes we use  $\tan^2x\ =\ \frac{\sin^2x}{\cos^2x}$  

Or  $\cot^2x=\frac{\cos^2x}{\sin^2x}$