Find the value of θ between 0° and 360° satisfying the equation 5 sin θ = 4
θ= sin-1(4/5)
= 53.13, 143.13
sinØ = 4/5 = .8
Your first angle is correct, so the angle in quad II should be 180-53.13 = 126.87°
check with a calculator, also check your second answer to see that it is incorrect.
To find the value of θ in the equation 5 sin θ = 4 between 0° and 360°, you need to use the inverse sine function, also known as arcsine (sin⁻¹).
Step 1: Divide both sides of the equation by 5 to isolate the sine function:
5 sin θ = 4
sin θ = 4/5
Step 2: Take the inverse sine (arcsine) of both sides of the equation to find θ:
θ = sin⁻¹(4/5)
Step 3: Use a calculator to find the value of the inverse sine. Make sure the calculator is set to degree mode.
Input sin⁻¹(4/5) in the calculator and calculate.
The result will give you the value of θ in radians. To convert it to degrees, multiply by (180/π).
Converting the result of θ to degrees, you will find two possible values because sine is periodic. The sine value repeats itself after every 360 degrees.
The result is:
θ ≈ 53.13° and θ ≈ 143.13°
So, the values of θ between 0° and 360° that satisfy the equation 5 sin θ = 4 are approximately 53.13° and 143.13°.