Podcast
Questions and Answers
What is the range of the function f(x) = cos(tan⁻¹(x))?
What is the range of the function f(x) = cos(tan⁻¹(x))?
- [0, 1]
- [-1, 0]
- [-1, 1]
- (0, 1] (correct)
What is the property of cos⁻¹(x) used in the given inequalities?
What is the property of cos⁻¹(x) used in the given inequalities?
- Cos⁻¹(x) is an increasing function
- Cos⁻¹(x) is an odd function
- Cos⁻¹(x) is a decreasing function (correct)
- Cos⁻¹¹(x) is a periodic function
What is the graph of the function y = cos(x) like in the interval [-π/2, π/2]?
What is the graph of the function y = cos(x) like in the interval [-π/2, π/2]?
- A constant function
- A straight line
- A decreasing curve
- An increasing curve (correct)
What is the range of tan⁻¹(x) in the given solution?
What is the range of tan⁻¹(x) in the given solution?
What is the purpose of multiplying both sides of the inequality by 3?
What is the purpose of multiplying both sides of the inequality by 3?
What is the domain of the function f(x) = cos(tan⁻¹(x))?
What is the domain of the function f(x) = cos(tan⁻¹(x))?
What is the range of the function f(x) = sin x?
What is the range of the function f(x) = sin x?
What is the domain of the function f(x) = cos^{-1} x?
What is the domain of the function f(x) = cos^{-1} x?
What is the value of sin^{-1} (1/2)?
What is the value of sin^{-1} (1/2)?
What is the property of the function f(x) = tan^{-1} x?
What is the property of the function f(x) = tan^{-1} x?
What is the graph of the function f(x) = sin^{-1} x?
What is the graph of the function f(x) = sin^{-1} x?
What is the range of the function f(x) = tan^{-1} x?
What is the range of the function f(x) = tan^{-1} x?
What is the value of cos^{-1} (√3/2)?
What is the value of cos^{-1} (√3/2)?
What is the property of the function f(x) = cos^{-1} x?
What is the property of the function f(x) = cos^{-1} x?
What is the domain of the function f(x) = tan x?
What is the domain of the function f(x) = tan x?
What is the graph of the function f(x) = cos x?
What is the graph of the function f(x) = cos x?
What is the range of the function $f(x) = an x$?
What is the range of the function $f(x) = an x$?
What is the value of $ an^{-1}(-3)$?
What is the value of $ an^{-1}(-3)$?
What is the value of $ an^{-1}(1) + rac{π}{2}$?
What is the value of $ an^{-1}(1) + rac{π}{2}$?
What is the value of $ an^{-1}(1) + rac{π}{2} + rac{π}{6}$?
What is the value of $ an^{-1}(1) + rac{π}{2} + rac{π}{6}$?
What is the value of $ an^{-1}(1) + rac{3π}{2} + rac{π}{6}$?
What is the value of $ an^{-1}(1) + rac{3π}{2} + rac{π}{6}$?
Study Notes
Inverse Trigonometric Functions
Domain, Range & Graph of ITF
- tan:
- Restricted Domain: (-π, π/2) ∪ (π/2, π)
- Range: ℝ
- cot:
- Restricted Domain: (0, π)
- Range: ℝ
- sec:
- Restricted Domain: (0, π) - π/2 - π
- Range: (-∞, -1] ∪ [1, ∞)
- cosec:
- Restricted Domain: (-π/2, 0) ∪ (0, π/2)
- Range: (-∞, -1] ∪ [1, ∞)
Examples
- cot⁻¹(0) = π/2
- cot⁻¹(1) = π/4
- cot⁻¹(-1) = 3π/4
Properties of Inverse Trigonometric Functions
- sin⁻¹(-x) = -sin⁻¹(x)
- cos⁻¹(-x) = π - cos⁻¹(x)
- tan⁻¹(-x) = -tan⁻¹(x)
- cot⁻¹(-x) = π - cot⁻¹(x)
- sec⁻¹(-x) = π - sec⁻¹(x)
- cosec⁻¹(-x) = -cosec⁻¹(x)
Graphs of Inverse Trigonometric Functions
- y = sin⁻¹(x)
- Domain: [-1, 1]
- Range: [-π/2, π/2]
- y = cos⁻¹(x)
- Domain: [-1, 1]
- Range: [0, π]
- y = tan⁻¹(x)
- Domain: ℝ
- Range: (-π/2, π/2)
Additional Examples
- Find the value of tan⁻¹(3) and tan⁻¹(-3)
- Solution: use the properties of inverse trigonometric functions to find the values.
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Description
Solve for θ when tangent inverse of -3 is equal to θ, where tangent of θ is equal to -3. Trigonometry problem involving inverse tangent function.
