Co-function Identities
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More Lessons for Trigonometry
Math Worksheets
In this lesson, we will look at co-function identities. What are the Co-function Identities?
A function f is cofunction of a function g if f(A) = g(B) when A and B are complementary angles.
sin A = cos(90° - A)
cos A = sin(90° - A)
sin A = cos B, if A + B = 90°
sec A = csc(90° - A)
csc A = sec(90° - A)
sec A = csc B, if A + B = 90°
tan A = cot(90° - A)
cot A = tan(90° - A)
tan A = cot B, if A + B = 90°
Cofunction Identities
This video explains the cofunction identities and how to determine cofunctions given a function value.
What is a cofunction.
Finding the cofunction.
Using the cofunction relationship
Examples:
Write each function in terms of its cofunction.
1. sin(18°)
2. tan(65°)
3. csc(84°)
Write each function in terms of its cofunction.
1. cos(π/4)
2. cot(π/3)
3. sec(&pi/6)
How to use cofunction identities to solve trigonometric equations? Examples:
Find a possible acute angle solution
cos(2θ + 16°) = sin(θ + 11°)
Find a possible acute angle solution
cot(θ) = tan(θ + π/6)
Cofunctions
Example:
If sin 72° = 0.9511
find cos 18°
Cofunction Identities in Trigonometry
The cofunction identities state that
The value of any trigonometric function at x is equal to the value of the cofunction at (π/2 - x).
cos(π/2 - x) = sin x
sin(π/2 - x) = cos x
tan(π/2 - x) = cot x
cot(π/2 - x) = tan x
sec(π/2 - x) = csc x
csc(π/2 - x) = sec x
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
More Lessons for Trigonometry
Math Worksheets
In this lesson, we will look at co-function identities. What are the Co-function Identities?
A function f is cofunction of a function g if f(A) = g(B) when A and B are complementary angles.
sin A = cos(90° - A)
cos A = sin(90° - A)
sin A = cos B, if A + B = 90°
sec A = csc(90° - A)
csc A = sec(90° - A)
sec A = csc B, if A + B = 90°
tan A = cot(90° - A)
cot A = tan(90° - A)
tan A = cot B, if A + B = 90°
Cofunction Identities
This video explains the cofunction identities and how to determine cofunctions given a function value.
What is a cofunction.
Finding the cofunction.
Using the cofunction relationship
Examples:
Write each function in terms of its cofunction.
1. sin(18°)
2. tan(65°)
3. csc(84°)
Write each function in terms of its cofunction.
1. cos(π/4)
2. cot(π/3)
3. sec(&pi/6)
How to use cofunction identities to solve trigonometric equations? Examples:
Find a possible acute angle solution
cos(2θ + 16°) = sin(θ + 11°)
Find a possible acute angle solution
cot(θ) = tan(θ + π/6)
Example:
If sin 72° = 0.9511
find cos 18°
Cofunction Identities in Trigonometry
The cofunction identities state that
The value of any trigonometric function at x is equal to the value of the cofunction at (π/2 - x).
cos(π/2 - x) = sin x
sin(π/2 - x) = cos x
tan(π/2 - x) = cot x
cot(π/2 - x) = tan x
sec(π/2 - x) = csc x
csc(π/2 - x) = sec x
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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