Inverse trigonometry is a branch of mathematics that deals with finding the angle measure, Cheat Sheet of Law

Download Inverse trigonometry is a branch of mathematics that deals with finding the angle measure and more Cheat Sheet Law in PDF only on Docsity! INVERSE TRIGONOMETRY Using the side lengths or ratios of a right triangle, inverse trigonometry is the discipline of mathematics that deals with determining the angles or ratios of the triangle. In contrast to regular trigonometry, which entails determining side lengths or ratios from angles, it is the opposite. Inverse trigonometric functions with the highest frequency are: * The function arcsine (sin1) determines the angle whose sine is a specified ratio. * The function arccosine (cos 1) locates the angle whose cosine is a specified ratio. * This function, arctangent (tan1), determines the angle whose tangent is a specified ratio. To demonstrate how to utilize inverse trigonometry, consider these examples: Find the angle whose sine is 0.5 in Example 1. The arcsine function gives us the answer sin(0.5) = 30°. Find the angle whose cosine is -0.8 in Example 2. The angle is in the second or third quadrant because the cosine is negative. Cos1(- 0.8) = 143.13° or 216.87° can be calculated using the arccosine function. Find the angle whose tangent is 2, as in Example 3. The arctangent function gives us the answer tan1(2) = 63.43°. The limits of the inverse trigonometric functions must be understood. They may not function for specific input values and can only find angles within a specified range. In addition, the inverse trigonometric functions are frequently stated in radians; hence, if necessary, convert to degrees. The inverse of conventional trigonometric functions are referred to as inverse trigonometric functions. With the trigonometric ratio value (sine, cosine, tangent, cosecant, secant, cotangent), they are utilized to get the angle measure. The symbols for these inverse functions are sin1, cos1, tan1, csc1, sec1, and cot1. Due to the periodic nature of inverse trigonometric functions, their range is constrained to a specific range. The inverse sine, cosine, and tangent functions have a range between -90° and 90°. Inverse trigonometric functions can be used in the following situations: Example 1: Given that sin(x) = 45°, determine the value of x. Solution: Using the inverse sine function's definition, we get sin(45°) = x. We obtain x = 2/2 since sin(45°) = 2/2.