# Inverse Trigonometric Functions – Form f(f⁻¹(x))

Inverse Trigonometric Functions – Form f(f⁻¹(x)) Function of the form f(f⁻¹(x)): where f(x) is Trigonometric Function (i)Consider function f(x) = sin(sin⁻¹x). Domain of the function is [-1, 1] Also, sin (sin ⁻¹(x)) = x sin(sin⁻¹x) = x for all x ϵ [-1, 1] (ii)Consider function f(x) = cos(cos⁻¹x). Domain of the function is [-1, 1] Read more about Inverse Trigonometric Functions – Form f(f⁻¹(x))[…]

# Relation f⁻¹(x) with f⁻¹(1/x) – 2

Relation f⁻¹(x) with f⁻¹(1/x) – 2 Theorem: cos⁻¹(1/x) = sec⁻¹(x), for all Proof: cos⁻¹(1/x) = sec⁻¹(x) Let sec⁻¹(x) = θ Where θ ϵ [0, π] –{0} and x = secθ 1/x = 1/ secθ 1/x = cosθ θ = cos⁻¹(1/x) sec⁻¹(x) = θ sec⁻¹(x) = cos⁻¹(1/x) cos⁻¹(1/x) = sec⁻¹(x), for all Hence proved Theorem: Proof: Read more about Relation f⁻¹(x) with f⁻¹(1/x) – 2[…]

# Relation f⁻¹(x) with f⁻¹(1/x) – 1

Relation f⁻¹(x) with f⁻¹(1/x) – 1 Theorem: sin⁻¹(1/x) = cosec⁻¹(x), for all , Proof: sin⁻¹(1/x) = cosec⁻¹(x) Let cosec⁻¹(x) = θ , And , x = cosecθ 1/x = 1/ cosecθ 1/x = sinθ θ = sin⁻¹(1/x) cosec⁻¹(x) = θ cosec⁻¹(x) = sin⁻¹(1/x) sin⁻¹(1/x) = cosec⁻¹(x), for all , Hence proved Examples: 1.sin⁻¹(1/2) = cosec⁻¹(2) Read more about Relation f⁻¹(x) with f⁻¹(1/x) – 1[…]

# Inverse Trigonometric Functions – cosec⁻¹(cosecx)

Inverse Trigonometric Functions – cosec⁻¹(cosecx) Graph y = cosec⁻¹(cosecx): y = cosec⁻¹(cosecx) cosecy = cosecx The general solution of cosecx = cosecα is nπ + α, n ϵ z Now general solution of cosecy = cosecx is y = nπ + x, n ϵ z y = nπ + x ….(1) Equation (1) Put n Read more about Inverse Trigonometric Functions – cosec⁻¹(cosecx)[…]

# Inverse Trigonometric Function – Graph cot⁻¹(cotx)

Inverse Trigonometric Function – Graph cot⁻¹(cotx) Graph y = cot⁻¹(cotx): y = cot⁻¹(cotx) coty = cotx The general solution of cotx = cotα is nπ + α, n ϵ z Now general solution of coty = cotx is y = nπ + x, n ϵ z y = nπ + x ….(1) Equation (1) Put Read more about Inverse Trigonometric Function – Graph cot⁻¹(cotx)[…]

# Graph of Inverse Trigonometric Function – cos⁻¹(cosx)

Graph of Inverse Trigonometric Function – cos⁻¹(cosx) Graph of y = cos⁻¹(cosx): y = cos⁻¹(cosx) cosy = cosx General solution is y = 2nπ ± x, n ϵ Z Now, with y ϵ [0, π] Draw plot the graph y = cos⁻¹(cosx) If n=0 y = 2πn ± x = 2π(0) ± x  = ± Read more about Graph of Inverse Trigonometric Function – cos⁻¹(cosx)[…]