4.3 Equivalent Trigonometric Expressions

Determine equivalent trigonometric expressions using right angle triangle :

Example :

sinx = a/b 

∠C = π/2 – x

sin ∠C = c/b

cos ∠C = a/b 

tan ∠C = c/a

Therefore,

sinx = cos ∠C , sinx = cos (π/2 – x)

Use unit circle along with transformations to derive equivalent trigonometric expressions that form other trigonometric identities, such as cos(π/2 + x ) = -sin x


Trigonometric Identities Featuring π/2

sin x = cos (π/2 – x)	cos x = sin (π/2 – x)	sin (π/2 + x ) = cosx	cos (π/2 + x ) =-sinx
tan x = cot (π/2 – x )	cot x = tan (π/2 – x )	tan (π/2 + x ) =-cotx	cot (π/2 + x ) =-tanx
csc x = sec(π/2 – x)	sec x = csc(π/2 – x)	csc (π/2 + x ) =secx	sec (π/2 + x )=-cscx