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Question

How do you find θ?


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Solution

Define θ in terms of inverse trigonometric ratios.

To find θ, consider a right-angled triangle, where the longest side is called the hypotenuse, and the sides opposite to the hypotenuse are referred to as the adjacent and opposite sides.

The six important inverse trigonometric functions (inverse trigonometric ratios) are calculated using the below formulas:

  • Inverse sine Function: θ=sin-1OppositesideHypotenuse
  • Inverse cosine Function :θ=cos-1AdjacentsideHypotenuse
  • Inverse tangent Function :θ=tan-1OppositesideAdjacentside
  • Inverse cosecant Function:θ=cosec-1HypotenuseOppositeside
  • Inverse secant Function : θ=sec-1HypotenuseAdjacentside
  • Inverse cotangent Function: θ=cot-1AdjacentsideOppositeside

Hence, to find θ the following formulas are used:

  • θ=sin-1OppositesideHypotenuse
  • θ=cos-1AdjacentsideHypotenuse
  • θ=tan-1OppositesideAdjacentside
  • θ=cosec-1HypotenuseOppositeside
  • θ=sec-1HypotenuseAdjacentside
  • θ=cot-1AdjacentsideOppositeside

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