I want to generate a sine wave from 2 data points, tmin and tmax. where tmin is where the sin wave starts, and the tmax is the top most point of the sine wave.

Then I want to find where tbase and tlimit intersect with the sine wave created in the previous step.

Example.

C = tlimit
B = tbase

I want to find area’s 1 and 2 (as in the example image)

currently, I’m able to calculate the area when tlimit is above tmax and tbase is less than or equal to tmin, just need help with this. here are my existing code but it may be wrong.

Existing Code

const calculateArea = (amplitude, meanTemp, threshold, start, end, steps = 1000) => {
    const dx = (end - start) / steps;
    let area = 0;
    for (let i = 0; i < steps; i++) {
        const x = start + (i * dx);
        const y = amplitude * Math.sin(x) + meanTemp;
        if (y > threshold) {
            const areaToAdd = (y - threshold) * dx;
            area += areaToAdd;
        }
    }
    return area;
}

// Called like
const tmean = (tmax + tmin) / 2;
const amplitude = (tmax - tmin) / 2;
const start = 0;
const end = 2 * Math.PI;
const area = calculateAreaThreshold(amplitude, tmean, tbase, start, end)

Test data (with results that may be wrong)

# Test Data 1
tmin = 5
tmax = 25
tbase = 10
tlimit = 30

current_returned_result = 39.610976908929906

# Test Data 2
tmin = 5
tmax = 25
tbase = 20
tlimit = 30

current_returned_result = 7.527554726471326

# Test Data 3
tmin = 5
tmax = 25
tbase = 15
tlimit = 22

current_returned_result = 24.679341500413543

I’ve been watching videos from Khan Academy on YT, about AP Calculus but I’m super lost