Nathan's Blog #2

A.) The relationship between sine and cosine is very easy. All you have to do is take the opposite of sine and you have cosine.

sin 0=0 - cos 0=1
sin pi/6=1/2 - cos pi/6=square root of 3/2
sin pi/4= square root of 2/2 - same for cos
sin pi/3=square root of 3/2 - cos pi/3=1/2
sin pi/2=1 - cos pi/2=0

B.) The next is tangent and cotangent. Tangent is the result of sin/cos. To get cotangent, just flip tangent.

tan 0=0 - cot 0=undefined
tan pi/6=square root of 3/3 - cot pi/6=square root of 3
tan pi/4=1 - same for cot
tan pi/3=square root of 3 - cot pi/3=square root of 3/3
tan pi/2=undefined - cot pi/2=0

C.) Our next pair is sine and cosecant. To find cosecant, just flip sine.

sin 0=0 - csc 0=undefined
sin pi/6=1/2 - csc pi/6=2
sin pi/4=square root of 2/2 - csc pi/4=square root of 2
sin pi/3=square root of 3/2 - csc pi/3=2 square root of 3/3
sin pi/2=1 - same for csc

D.) Cosine and secant are alike because all you have to do to find secant, is flip cosine.

cos 0=1 - same for sec
cos pi/6=square root of 3/2 - sec pi/6=2 square root of 3/2
cos pi/4=square root of 2/2 - sec pi/4=square root of 2
cos pi/3=1/2 - sec pi/3=2
cos pi/2=0 - sec pi/2=undefined

E.) The last relationship of the six trigonomic funtions is between sine, cosine, and tangent. To find cosine, it is the opposite of sine, and to find tangent, divide sine by cosine.

sin 0=0 - cos 0=1 - tan 0=0
sin pi/6=1/2 - cos pi/6=square root of 3/2 - tan pi/6=square root of 3/3
sin pi/4=square root of 2/2 - same for cosine - tan pi/4=1
sin pi/3=square root of 3/2 - cos pi/3=1/2 - tan pi/3=square root of 3
sin pi/2=1 - cos pi/2=0 - tan pi/2= undefined