Solve this equation. Give a general formula for all the solutions using k to represent your arbitrary integer.
sin θ = 1/2
θ =
sin ¥è = 1/2
¥è=90 or pi/2
only positive on pi/2
¥è=pi/2+2kpi
my question How to solve If θ and 3θ -30° are acute angles such that sinθ=cos(3θ-30°)then find the value of tanθ
To solve the equation sin θ = 1/2, we need to determine the values of θ that satisfy this equation. Remember that the sine function represents the ratio of the opposite side to the hypotenuse in a right triangle.
To find the solution, we can use the inverse sine function, also known as arcsine or sin^(-1). Taking the inverse sine of both sides of the equation, we have:
arcsin(sin θ) = arcsin(1/2)
θ = arcsin(1/2)
The inverse sine function gives us the principal value of θ that satisfies the equation sin θ = 1/2. This value is typically expressed in radians.
The principal value of arcsin(1/2) is π/6 radians or 30 degrees. However, the sine function has multiple solutions, so we can find additional solutions by considering the periodic nature of the sine function.
Since sin (θ + 2πk) = sin θ for any integer k, we can generalizethe solutions by using k as an arbitrary integer. The general formula for all the solutions can be expressed as:
θ = π/6 + 2πk
Where k represents any integer value, and each value of k will yield a different solution for θ.