how to use trignometry in quadrtic equation

Asked by Gyana Ranjan | 25th Oct, 2015, 10:21: PM

Expert Answer:

C o n s i d e r space a n space e x a m p l e colon F i n d space a l l space s o l u t i o n s space o f space 2 sin squared x minus sin x minus 1 equals 0 space i n space t h e space i n t e r v a l space left square bracket 0 comma space 2 straight pi right parenthesis.  Solution colon Consider space the space given space equation comma space 2 sin squared straight x minus sinx minus 1 equals 0 This space is space straight a space quadratic space in space sinx Let space straight y equals sinx Substituting space straight y equals sinx space in space the space above space equation comma space we space have comma 2 straight y squared minus straight y minus 1 equals 0 rightwards double arrow 2 straight y squared minus 2 straight y plus straight y minus 1 equals 0 rightwards double arrow 2 straight y open parentheses straight y minus 1 close parentheses plus open parentheses straight y minus 1 close parentheses equals 0 rightwards double arrow open parentheses 2 straight y plus 1 close parentheses open parentheses straight y minus 1 close parentheses equals 0 rightwards double arrow 2 straight y plus 1 equals 0 space or space straight y minus 1 equals 0 rightwards double arrow 2 straight y equals negative 1 space or space straight y equals 1 rightwards double arrow straight y equals fraction numerator negative 1 over denominator 2 end fraction space or space straight y equals 1 rightwards double arrow sinx equals fraction numerator negative 1 over denominator 2 end fraction space or space sinx equals 1 rightwards double arrow straight x equals fraction numerator 7 straight pi over denominator 6 end fraction comma fraction numerator 11 straight pi over denominator 6 end fraction space or space straight x equals straight pi over 2

Answered by Vimala Ramamurthy | 26th Oct, 2015, 11:26: AM