Solving Right Triangles Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems.

Unit J2 Inverse Functions  In Algebra, when we have a function f(x) such as, we can find a function called the inverse function by exchanging places with the x and the y.  In this case, if we exchange places with the x and the y, we will get the following function: or change it to which would be the inverse function.

Unit J3 Inverse Functions  In the previous lesson, we learned that the trig function of sin 30º = 0.5.  We want a function that will tell us that an angle that has a sine of 0.5 would be 30º.  This is written as sin -1 (0.5) = 30º and is called an inverse function.  For each of the three trigonometric functions, there is an inverse function.

Unit J4 Inverse Functions  To find the inverse function for think of the angle as the x and the as the y.  Now change places with the x and the y:  To access the inverse trig functions on your calculator use and then,, or. 2ND SIN COS TAN

Unit J5 Key Concepts: Get Organized Trig FunctionInverse Trig Function sine sin A = sin -1 = m ∠ A cosine cos A = cos -1 = m ∠ A tangent tan A = tan -1 = m ∠ A B C A 5 3 4

Unit J6 Example of Inverse Functions  Use the given sides to find the measure of angle A.  You could use the sine, cosine or tangent function to find the answer. sin A = ( ) use: sin -1 ( ) = 53º cos A = ( ) use: cos -1 ( ) = 53º tan A = ( ) use: tan -1 ( ) = 53º B C A No matter which function you use, you will get 53º.

Unit J7 Inverse Functions  When you know the degrees of the angle and you need to find the missing side, you will use one of the functions: or.  When you know the side lengths of the triangle and you need to find a missing angle, we will use one of the inverse functions:

Unit J8 Lesson Quiz Use your calculator to find each angle measure to the nearest degree. 1. cos -1 (0.97) 2. tan -1 (2) 3. sin -1 (0.59) Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 14° 63° 36° DF  5.7; m  D  68°; m  F  22° AC  0.63; BC  2.37; m  B = 15° 4. 5.