How do you solve \sin x=-\frac12 ?

Sandra Allison

Sandra Allison

Answered question

2021-12-30

How do you solve sinx=12 ?

Answer & Explanation

Bernard Lacey

Bernard Lacey

Beginner2021-12-31Added 30 answers

Explanation:
sinx is negative in the 3-rd and 4-th quadrants. Since
sinπ6=12
sinx would be 12 for x=π+π6 and for x=2ππ6
The Principal so;ution is this
x=7π6,11π6

karton

karton

Expert2022-01-08Added 613 answers

Take the inverse sine of both sides of the equation to extract x from inside the sine.
x=arcsin(12)
The exact value of arcsin(12) is π6
x=π6
The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from 2π, to find a reference angle. Next, add this reference angle to π to find the solution in the third quadrant.
x=2π+π6+π
Simplify the expression to find the second solution.
x=7π6
Find the period
2π
Add 2π to every negative angle to get positives angles.
x=11π6
The period of the sin(x) function is 2π so values will repeat every 2π radians in both directions.
x=7π6+2πn, 11π6+2πn, for any integer n

user_27qwe

user_27qwe

Skilled2022-01-08Added 375 answers

Thanks. It's helped me.

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