cofunction identities
sin (π/2 – θ) = cosθcos (π/2-θ) = sinθtan (π/2-θ) = cotθcot (π/2-θ) = tanθsec (π/2-θ) = cscθcsc (π/2-θ) = secθ
Cofunction identities are a set of trigonometric identities that relate the trigonometric functions of complementary angles, which are angles that add up to 90 degrees. The six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. The cofunction identities express the relationship between two complementary angles when the trigonometric functions of those angles are interchanged.
The six cofunction identities can be written as follows:
1. sin(theta) = cos(90-theta)
2. cos(theta) = sin(90-theta)
3. tan(theta) = cot(90-theta)
4. cot(theta) = tan(90-theta)
5. sec(theta) = csc(90-theta)
6. csc(theta) = sec(90-theta)
These identities can be used to simplify trigonometric expressions and convert one function into another. For example, if we need to find the value of cos(60 degrees), we can use the first cofunction identity to write cos(60) = sin(30) = 1/2.
It is important to note that these identities only apply to complementary angles, and cannot be used for other angles. Also, we need to use the correct units for the angles, which could be degrees or radians.
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