TRIGONOMETRIC EQUATIONS - Exercise 4

Solve the equation tex2html_wrap_inline65 . Restrict solutions to the interval tex2html_wrap_inline67 .

Solution: The substitution tex2html_wrap_inline69 yields the equation tex2html_wrap_inline71 , which is quadratic in u. We use the quadratic formula to solve for tex2html_wrap_inline69 :

displaymath63

If tex2html_wrap_inline77 the calculator gives x=1.1191 as the acute solution, so we deduce that the other solution is tex2html_wrap_inline81 . The equation tex2html_wrap_inline83 has no solutions, since tex2html_wrap_inline85 for all x. The solution set is therefore tex2html_wrap_inline89 .

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Luis Valdez-Sanchez
Tue Dec 3 17:39:00 MST 1996

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