Reciprocal trigonometric functions magnify what happens when sine or cosine approaches zero.
WHAT HAPPENS IF…Is cotangent defined at 90°?
Interactive exploration
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Connect the picture to the ideasecθ=cosθ1,cscθ=sinθ1,cotθ=sinθcosθ
These definitions apply only when their denominators are nonzero. Secant is undefined at odd multiples of π/2; cosecant and cotangent are undefined at integer multiples of π. Cotangent can be defined where tangent is not, so 1/tan is not a complete domain description.
A detail that matters
Reciprocal and inverse trigonometric functions are different operations.