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Trigonometry

Using Inverse Trigonometric Functions to Solve for Angles

The inverse trigonometric functions \(\sin^{-1}(x), cos^{-1}(x), tan^{-1}(x), \) are used to find the unknown measure of an angle of a right triangle when two side lengths are known. 

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Step 1

Identify the sides in relation to the angle. In the diagram above, 6750 is the adjacent side in relation to angle \(a^{\circ}\), and 8100 is the hypotenuse side.

Step 2

Use the appropriate trigonometric ratio. Since the adjacent and hypotenuse sides are given, \(\cos^{-1}(x)\) is the appropriate inverse function.

Step 3

Perform the Calculations. \[\cos^{-1}\left(\frac{6750}{8100}\right) = 33.557^{\circ} \simeq 33.6^{\circ} \]

Take note that the angle setting in your calculator will determine the output measurement. Setting your calculator to degrees will give an answer in degrees. Whereas, radian mode will calculate answer in terms of radians.

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