function love.load()
    --Object = require "classic"
    require "cjrcle"
    windowwidth = 1000
    windowheight = 1000
    love.graphics.setBackgroundColor(0, 0, 0)
    sucess = love.window.setMode(windowwidth, windowheight)

    ctheta = math.pi/2
    x = 0
    y = 0
    b = math.pi/ctheta

    sinxloc = 0
    startposX = 0
    discr = 50
    hr = 10

    speed = 1

    thrown = false -- a variable to check if the hammer has been let go

    -- hammer position
    hxpos = startposX + discr*math.cos(math.pi/2)/math.pi
    hypos = y - discr*math.sin(math.pi/2)
    nxpos = hxpos
    nypos = hypos
    rv = 1 -- rotational velocity

    --m = -hxpos/math.sqrt(50*50 - hxpos*hxpos)/discr
    --dYdX = -hxpos/math.sqrt(discr*discr - hxpos*hxpos)/discr
    dYdX = ctheta + math.pi/2
end

--[[
  equation of tangent line y = -x + 50*math.sqrt(2)
]]

function love.keypressed(key)
    if key == "space" then
        thrown = true
    end
    if key == "r" then
        b = math.pi/2
    end
end

function love.update(dt)
    --[[
        user sialek suggestion
        you never update dYdX beyond the initial value
        it's only at the end of the love.load() function
        putting the formula you have in the update function doesn't work either
        if you set it to a fixed value that it does actually go in some other direction
        i think you need to add a line to update dYdZ in your actual update function and rework how you're calculating it
            the one up top is using discr, which never changes, so that's probably why it doesn't help in the update() function

        maccraft123 suggestion
        try representing the position of the hammer in polar coordinates
        for rendering it convert it to cartesian
    ]]

    ctheta = ctheta - rv*math.pi*dt/30 -- change in theta
    --ntheta = ctheta -- theta now
    if ctheta < ctheta - 2*math.pi then
        ctheta = math.pi/2
    end

    if not thrown then
        ctheta = ctheta -rv*math.pi*dt/30
        hxpos = startposX + discr*math.cos(ctheta) -- this snippet of code calculates the hammer position for the next frame... dX/dY
        hypos = y - discr*math.sin(ctheta)
        ntheta = ctheta -- keep track of the current value of the change is theta with the current value of theta
    end
    if thrown == true then -- the tangent line is π/2 radians from ctheta
        ctheta = ntheta
        index = 0
        -- trying to get the hammer to go in a straight line from it's current position to 1/cos(ctheta)
        if index%2 == 0 then
            if hxpos < windowwidth/2 and hypos < windowheight/2 and hxpos > -1*windowwidth/2 and hypos > -1*windowheight/2 then
                hxpos = hxpos + 1
                --hypos = hypos - dYdX

            --if hxpos < discr/math.cos(ctheta) then -- if the x coordinate of the hammer is less than the secant of ctheta
                --hxpos = hxpos + math.tan(ntheta)
                --hypos = hypos/hxpos
                hypos = hypos + dYdX -- hypos will never reach 0 because the cot(ctheta) will never be 0
                --hypos = hypos + math.tan(ntheta)
            end
        end
        if index%2 ~= 0 then
            --if hxpos < discr/math.sin(ctheta) then -- if the x coordinate of the hammer is less than the cosecant of ctheta
            if hxpos < windowwidth/2 or hxpos > -windowwidth/2 then
                hxpos = hxpos + 1
                hypos = hypos + dYdX
                --hypos = hxpos + hypos/hxpos
                index = index + 1
                -- y never gets to 1 because the tangent is never
            end
        end

        --[[
        hxpos = hxpos + 50*dt*10*math.cos(ntheta)
        hypos = hxpos*hxpos/math.sqrt(50^2 + hxpos*hxpos) - 50*math.cos(ntheta) - hypos-- + hxpos -- hypos is now equal to dx/dy at ntheta
        cjrcle(10, hxpos, hypos)
        ]]
    end

    local m = math.pow(2, dt)
    if love.keyboard.isDown("up") then
        b = b*m   --the period of the sine wave is  pi/delthe... i think?
    end
    if love.keyboard.isDown("down") then
        b = b/m
    end
end


function arccirc(r, x, y, delthe)
    arcang = math.atan(y + r/x + r)
	for theta = 0, arcang, delthe do
		love.graphics.line(discr*math.cos(theta) + x, discr*math.sin(theta) + y, discr*math.cos(theta + delthe) + x, discr*math.sin(theta + delthe) + y)
	end
end

function love.draw()

    love.graphics.translate(windowwidth/2, windowheight/2)
    love.graphics.setColor(1, 1, 0)
    love.graphics.print("sine = " .. -hypos/50, -400, -400)
    love.graphics.setColor(1, 0, 0)
    love.graphics.print("cosine = " .. hxpos/50, -400, -390)
    love.graphics.setColor(0, 0, 1)
    love.graphics.print("tangent = " .. math.tan(ctheta), -400, -380)
    love.graphics.setColor(1,.6,.5)
    love.graphics.print("cotangent = " .. 1/math.tan(ctheta),-400, -370)
    love.graphics.setColor(0,1,0)
    love.graphics.print("secant = " .. 1/math.cos(ctheta), -400, -360)
    love.graphics.setColor(1,0,1)
    love.graphics.print("cosecant = " .. 1/math.sin(ctheta) , -400, -350)
    love.graphics.setColor(1,1,1)
    love.graphics.print("b: " .. b, -400, -340)
    love.graphics.print("Ø: ".. ctheta .. " radians, or ", -400, -330 )
    love.graphics.print("which is also " .. ctheta*180/math.pi .. " degrees!", -400, -300)
    love.graphics.print("the derrivative of the quation X^2 + Y^2 = r^2 @ r = 50: ", -400, -280)
    love.graphics.print("dY/dX = -x^2/(math.sqrt(50^2 - x) + 2500) = " .. -hxpos*hxpos/(math.sqrt(discr*discr - hxpos) + 2500), -400, -260)
    love.graphics.print("tangent line has equation: ", -400, -240)
    love.graphics.print("Y = mX + b", -400, -220)

    love.graphics.print("Y = " .. dYdX .. "*" .. hxpos .. " + B", -400, -200)
    love.graphics.print("B = " .. -dYdX, -400, -190)

    love.graphics.print("Tangent line has equation:", -400, -150)

    love.graphics.print("Y = " .. dYdX .. "X + " .. -dYdX, -400, -130)

    love.graphics.print("The value of thrown is: ", -400, -120)
    if thrown then
        love.graphics.print("thrown!", -200, -120)
    else
        love.graphics.print("not thrown:(", -200, -120) -- thrown not being updated:()
    end


    -- orange cjrcle

    love.graphics.setColor(.7, .6, .3)
    cjrcle(discr, startposX, 0, 32)

    -- blue cjrcle for player
    love.graphics.setColor(1, 1, 1)
    cjrcle(10, hxpos, hypos)


    -- violet tangent and cotantgent lines
    --orange cotangent...
    love.graphics.setColor(1,.6,.5)
    love.graphics.line(50*math.cos(ctheta), -50*math.sin(ctheta), 0, -50/math.sin(ctheta))
    -- blue tangent
    love.graphics.setColor(0, 0, 1)
    love.graphics.line(50*math.cos(ctheta), -50*math.sin(ctheta), 50/math.cos(ctheta), 0)

    --grey continued gray tangent line
    love.graphics.setColor(.5,.5,.5)
    love.graphics.line(discr/math.cos(ctheta), 0, windowwidth/2, windowwidth/2*(math.sqrt(discr*discr - hxpos*hxpos))/50)

    love.graphics.setColor(.8,.8,.8)
    love.graphics.line(discr/math.cos(ctheta), 0, windowwidth/2*(math.sqrt(discr*discr - hxpos*hxpos))/discr, windowwidth/2)

    -- secant and cosecant
    love.graphics.setColor(1, 0, 1)
    love.graphics.line(0,0,0,-50/math.sin(ctheta)) --csc
    love.graphics.setColor(1, 1, .1)
    love.graphics.setColor(0, 1, 0)
    love.graphics.line(0,0,50/math.cos(ctheta),0) --sec

    --different triangle

    --red horizontal cosine line
    love.graphics.setColor(1, 0, 0)
    love.graphics.line(0, 0, hxpos, 0)

    -- yellow vertical sine line
    love.graphics.setColor(1, 1, 0)
    love.graphics.line(hxpos, hypos, 50*math.cos(ctheta), 0)


    -- radius
    love.graphics.setColor(.5, .3, 0)
    love.graphics.line(0, 0, hxpos, hypos)




    --anglethetaprints

    love.graphics.print("Ø",hxpos/2, hypos)
    for thetarc = math.atan2(hypos,hxpos), math.sin(ctheta), -math.pi/60 do

        love.graphics.setColor(0,1,0)
        if hxpos > 0 and hypos > 0 then
            if thetarc <= math.pi/2 and thetarc > 0 then
                love.graphics.line(10*math.cos(thetarc), 10*math.sin(thetarc), 10*math.cos(thetarc + math.pi/60), 10*math.sin(thetarc + math.pi/60))
                thetarc = thetarc + math.pi/60
                --love.graphics.print("Ø",hxpos/2, hypos/2)
            end
        end

        if hxpos < 0 and hypos > 0 then
            if thetarc <= 0 and thetarc > -math.pi/2 then
                love.graphics.line(-10*math.cos(thetarc), -10*math.sin(thetarc), -10*math.cos(thetarc + math.pi/60), -10*math.sin(thetarc + math.pi/60))
                thetarc = thetarc + math.pi/60
                --love.graphics.print("Ø",hxpos/2, hypos/2)
            end
        end

    end

    --sinecurve

    sinxloc = 50
    cosyloc = 50
    love.graphics.setColor(1, 0, 0.4)
    for theta = -32*math.pi, 32*math.pi, math.pi/180 do
        love.graphics.line(25 + sinxloc, -50*math.sin(b*theta), 25 + sinxloc + math.pi/360, -50*math.sin(b*theta + math.pi/360))
        sinxloc = sinxloc + 1
        cosyloc = cosyloc + 1
    end


    love.graphics.setColor(1,0,0)


    love.graphics.print("x: " .. hxpos/50, hxpos - 50, hypos)
    love.graphics.print("y: " .. -hypos/50, hxpos - 50, hypos+10)

end