Solve the trigonometric equation3sin(2𝑡)+4=1

Sure, let's solve the trigonometric equation step by step.

The given equation is 3sin(2t) + 4 = 1.

Step 1: Subtract 4 from both sides of the equation to isolate the trigonometric function.

3sin(2t) = 1 - 4

3sin(2t) = -3

Step 2: Divide both sides of the equation by 3 to solve for sin(2t).

sin(2t) = -3/3

sin(2t) = -1

Step 3: Now, we need to find the value of 2t. The sine function equals -1 at 3π/2 + 2nπ, where n is an integer.

2t = 3π/2 + 2nπ

Step 4: Finally, divide both sides of the equation by 2 to solve for t.

t = (3π/2 + 2nπ) / 2

t = 3π/4 + nπ

So, the solutions to the equation are t = 3π/4 + nπ, where n is an integer.