EXAMPLE 4 Determining Whether a Value Is in the Range of a Trigonometric Function Decide whether each statement is possible or impossible. (a) sine =2.5 (b) tane =110.47 (c) sece =0.6 EXAMPLE 5 Finding All Function Values Given One Value and the Quadrant Suppose that angle & is in quadrant II and sing = =. Find the values of the other five trigonometric functions. Pythagorean Identities Pythagorean Identities For all angles & for which the function values are defined, the following identities hold sim '8 + cos's =1 tan '8 +1= sec's 1+ cot'd = cache Reflect: Give an alternative form of each Pythagorean identity listed above.1-18 Chapter 1 Trigonometric Functions Quotient Identities Quotient Identities For all angles & for which the denominators are not zero, the following identities hold sine -= tane -=Cole cose sing EXAMPLE 6 Using Identities to Find Function Values Find sing and tand. given that cose = - and sine 3 0. Reflect: In Examples 3 and 6, how are the correct signs chosen when square roots are rakan? EXAMPLE 7 Using Identities to Find Function Values Find sine and cose, given that tano = + and & is in quadrant