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 area1 = calculateAreaThreshold(amplitude, tmean, tbase, start, end)
const area2 = calculateAreaThreshold(amplitude, tmean, tlimit, start, end)
return area1 + area2;

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

Update 1

I have tmin, tmax these are the values needed to generate the sine wave. then i have tbase and tlimit which intersect the sine wave.

I want to calculate the area for the blue shaded part labeled 1 and 2.

t is unknown (its the time, horizontal axis) and c^ (c with a circle) is just the y axis.

I only have those 4 values to work with, a 5th value which is the mean such as (tmax + tmin) / 2

Update 2

ChatGPT gave me this, but I don’t think this is right at all.

M = (T_max + T_min) / 2
A = (T_max - T_min) / 2
t1 = 12 - (24 / (2 * math.pi)) * math.asin((tbase - M) / A)
t2 = 12 + (24 / (2 * math.pi)) * math.asin((tbase - M) / A)
area_1 = (A * math.cos(math.pi * (t1 - 12) / 12) + M - tbase) * (12 - t1)
area_2 = (A * math.cos(math.pi * (t2 - 12) / 12) + M - tbase) * (t2 - 12)
area = (area_1 + area_2) / 24

Update 3

Reason for getting the areas, I need to calculate these area’s for a project at work as its related to GDD (Growing degree days). so the tmin and tmax are min and max values for a day. tbase and tlimit are the are unique to each crop.

The sine wave would start at x = 0 and y = tmin, the peak of the sine wave would reach y = tmax

Update 4

after reviewing the suggested documents / links. and chatting with ChatGPT

I’ve managed to come up with this function

const calculateSineArea = (tmin, tmax, tbase, tlimit) => {
        const amplitude = (tmax - tmin) / 2;
        const angleBase = Math.asin((tbase - tmin) / amplitude) * (180 / Math.PI);
        const angleLimit = Math.asin((tlimit - tmin) / amplitude) * (180 / Math.PI);
        const areaBase = (Math.PI / 180) * angleBase * amplitude;
        const areaLimit = (Math.PI / 180) * angleLimit * amplitude;
        const finalArea = (areaLimit - areaBase) * amplitude;
        return finalArea;
    } 

but I get 0 returned

here are the few tests I’ve done

Test 1

// inputs
tmin:5, tmax:25, tbase:10, tlimit:30
// calculated
amplitude:10, angleBase:30.000000000000004, angleLimit:NaN, areaBase:5.23598775598299, areaLimit:NaN, finalArea:NaN

Test 2

// inputs
tmin:5, tmax:25, tbase:20, tlimit:30
// calculated
amplitude:10, angleBase:NaN, angleLimit:NaN, areaBase:NaN, areaLimit:NaN, finalArea:NaN

Test 3

// inputs
tmin:5, tmax:25, tbase:15, tlimit:22
// calculated
amplitude:10, angleBase:90, angleLimit:NaN, areaBase:15.707963267948966, areaLimit:NaN, finalArea:NaN