Key to "How are the inverse trigonometric functions defined? How..."

cleritere39

Answered question

2021-11-23

How are the inverse trigonometric functions defined? How can you sometimes use right triangles to find values of these functions? Give examples.

Answer & Explanation

Geraldine Flores

Beginner2021-11-24Added 21 answers

Step 1
Inverse trigonometric function:
It is defined as that the anti or arcus function of the function is known as the inverse trigonometry function.
For examples:
sine, cosine, cosecant, tangent, secant and cotangent.
Step 2
Let‘ABC’ be right angle triangle.

Step 3
In the right-angle triangle ABC,

\sin θ = \frac{A B}{A C} = \frac{y}{\sqrt{x^{2} + y^{2}}} \Rightarrow θ = \sin^{- 1} (\frac{y}{\sqrt{x^{2} + y^{2}}})

\cos θ = \frac{B C}{A C} = \frac{x}{\sqrt{x^{2} + y^{2}}} \Rightarrow θ = \cos^{- 1} (\frac{x}{\sqrt{x^{2} + y^{2}}})

\tan θ = \frac{A B}{B C} = \frac{y}{x} \Rightarrow θ = \tan^{- 1} (\frac{y}{x})

\cot θ = \frac{B C}{A B} = \frac{x}{y} \Rightarrow θ = \cot^{- 1} (\frac{x}{y})

\sec θ = \frac{A C}{B C} = \frac{\sqrt{x^{2} + y^{2}}}{x} \Rightarrow θ = \sec^{- 1} (\frac{\sqrt{x^{2} + y^{2}}}{x})

\csc θ = \frac{A C}{A B} = \frac{\sqrt{x^{2} + y^{2}}}{y} \Rightarrow θ = \csc^{- 1} (\frac{\sqrt{x^{2} + y^{2}}}{y})

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