SOLUTION: Determine the exact value of x. In other words, your answer must not use decimals cos⁡2x-sin⁡x=0
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Question 1110695: Determine the exact value of x. In other words, your answer must not use decimals cos2x-sinx=0
Found 2 solutions by greenestamps, Fombitz:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
You have three identities for cos(2x):
Since the other term in the equation is sin(x), you want to use the identity for cos(2x) that contains only sin(x); that will give you a quadratic equation in sin(x). So
or
The wording of the question is strange: "Determine the exact value of x." There are an infinite number of values of x that satisfy the equation....
For solutions on the interval [0,2pi), the solutions are {pi/6, 5pi6, 3pi/2}.
A graph:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Use a substitution,
So,
Two "u" solutions:
and
and
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