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Master Trigonometry with These Essential Practice Questions
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Try this:
##-1\le \cos x \le 1##
##-\frac 5 4 \le \cos x - \frac 1 4 \le \frac 3 4##
##0\le (\cos x - \frac 1 4)^2 \le \frac {25} {16}##
##0\ge -2(\cos x - \frac 1 4)^2\ge -\frac {25} 8##
##\frac 9 8 \ge \frac 9 8 -2(\cos x - \frac 1 4)^2\ge -\frac {16} 8 = -2##
Think about what that gives.
##-1\le \cos x \le 1##
##-\frac 5 4 \le \cos x - \frac 1 4 \le \frac 3 4##
##0\le (\cos x - \frac 1 4)^2 \le \frac {25} {16}##
##0\ge -2(\cos x - \frac 1 4)^2\ge -\frac {25} 8##
##\frac 9 8 \ge \frac 9 8 -2(\cos x - \frac 1 4)^2\ge -\frac {16} 8 = -2##
Think about what that gives.