Question
Solve the equation
x={12π+kπ125π+kπ,k∈Z
Alternative Form
x={15∘+180∘k75∘+180∘k,k∈Z
Alternative Form
x≈{0.261799+kπ1.308997+kπ,k∈Z
Evaluate
sin(2x)=21
Use the inverse trigonometric function
2x=arcsin(21)
Calculate
2x=6π2x=65π
Add the period of 2kπ,k∈Z to find all solutions
2x=6π+2kπ,k∈Z2x=65π+2kπ,k∈Z
Calculate
More Steps

Evaluate
2x=6π+2kπ
Divide both sides
22x=26π+2kπ
Divide the numbers
x=26π+2kπ
Divide the numbers
x=12π+kπ
x=12π+kπ,k∈Z2x=65π+2kπ,k∈Z
Calculate
More Steps

Evaluate
2x=65π+2kπ
Divide both sides
22x=265π+2kπ
Divide the numbers
x=265π+2kπ
Divide the numbers
x=125π+kπ
x=12π+kπ,k∈Zx=125π+kπ,k∈Z
Solution
x={12π+kπ125π+kπ,k∈Z
Alternative Form
x={15∘+180∘k75∘+180∘k,k∈Z
Alternative Form
x≈{0.261799+kπ1.308997+kπ,k∈Z
Show Solution
