Common Trigonometry Mistakes
Example: Solve a trigonometric equation |
Some problems provide the opportunity for more than one mistake. The Goal
Solve the equation:
The Mistakes
Find the mistakes:
(Roll the mouse over the math to see a hint in red)
(Roll the mouse over the math to see a hint in red)
(Roll the mouse over the math to see a hint in red)
The Correction
(Roll the mouse over the area above to see the correction in blue) Explanations In the first mistake the coefficients of cos2(2x) and sin2(x) mysteriously vanished in the first step. The second attempted solution makes use of an incorrect formula for cos(2x), in fact the negation of a correct formula. In the third mistake once again an incorrect formula was used for cos(2x); recall that in fact cos2(x) + sin2(x) = 1, not cos(2x). The keys to solving this problem are knowing the correct double angle formulas and then using correct algebra to solve the equation. |
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