Cofunction Identities
For example: Given that the the complement of
Radians
Sine and cosine are cofunctions and complements 


Tangent and cotangent are cofunctions and complements 


Secant and cosecant are cofunctions and complements 


Degree
Sine and cosine are cofunctions and complements 
sin(90°  x) = cos x 
cos(90°  x) = sin x 
Tangent and cotangent are cofunctions and complements 
tan(90°  x) = cot x 
cot(90°  x) = tan x 
Secant and cosecant are cofunctions and complements 
sec(90°  x) = csc x 
csc(90°  x) = sec x 
Degree Example:
sin A = cos B =
A = B =
cos(22.6°) = sin(67.5)°
Therefore, the value of cosine B is equal to sine A which is the cofunction and complement of B. The process remains the same whether you are in degree mode or radian mode.
Let's see how this can be applied.
Use the cofunction identities to evaluate the expression without a calculator!
sin^{2} (23°) + sin^{2} (67°)
Step 1: Note that 23° + 67° = 90° (complementary)
Step 2: use the cofunction identity and let x = 23°sin(90°  x) = cos x
therefore sin(67°) = cos(23°)
Step 3: use substitution sin^{2}(23°) + cos^{2}(23°)
Step 4: use the Pythagorean identity sin^{2}θ + cos^{2}θ = 1sin^{2}(23°) + cos^{2}(23°) = 1
Therefore, sin^{2}(23°) + sin^{2}(67°) = sin^{2}(23°) + cos^{2}(23°) = 1
Related Links: Math Trigonometry Sum and Difference of Angles Identities Trigonometric Identities  Reciprocal Identities 
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