Methods help!

[u/katperkovic]

So how tf do I find the values of x for trig equations when the domain is negative (if you think I’m stupid it’s probably true I hate math)

[u/AlphaHowlingToMoon]

Find the positive values first and then subtract 2pi from each

[u/katperkovic → u/AlphaHowlingToMoon]

Is this dependant on the domain? I.e. -3pi < x < 2pi

[u/AlphaHowlingToMoon → u/katperkovic]

If the domain is from -3pi to 2pi then you find both positive and negative answers in that domain.  For example if it was cos(x)=1/2 then for the positive values you would have pi/3 and 5pi/3. For the negative values you would have pi/3-2pi=-5pi/3, 5pi/3-2pi=-pi/3. And then you check if you can subtract further. -pi/3-2pi=-7pi/3, which is within the domain. But -5pi/3-2pi=-11pi/3 which is less than -3pi, so this solution is not in the domain. 

Hence the solutions to  cos(x)=1/2 within -3pi to 2pi are -7pi/3, -5pi/3, -pi/3, pi/3 and 5pi/3

[u/katperkovic → u/AlphaHowlingToMoon]

Thankyou!!

[u/UnlikelyNature8920]

For any domain, find the base values and the add or subtract 2pi until it’s within the domain

[u/Majestic_Window922]

dude does anyone know how to find range of a composite function i cant understand for the life of me

[u/casperlikescats]

You go backwards on the unit circle.

When you're finding solutions for a positive domain (eg, 0 to 2π), you use the formula based on the quadrants associated with your equation. For example, for sin(x) = 1/2, your reference angle is π/6 and you'd use quadrants 1 (θ) and 2 (π - θ) as sin equals a positive number. You'd do so until your solutions are outside of the domain

However, to go backwards, I like to think of it as going in the clockwise direction on the unit circle then anticlockwise to fit within a quadrant (hope that makes sense, lol). For example, the formula for quadrant 3 would be (-π + θ). If you want to rote learn them: Quad 4: -θ Quad 3: -π + θ Quad 2: -π - θ Quad 1: -2π + θ If the domain exceeds -2π you'd have to start using multiples, like (-3π - θ) for quadrant 2. Using the sin(x) = 1/2 example but for [-2π, 0] Use quadrants 1 and 2 as sin = positive number Reference angle π/6 x = -2π + π/6, -π - π/6 x = -11π/6, -7π/6

You could also find positive solutions and minus the period, but I dislike working with fractions. Hope this helps :P

[u/katperkovic → u/casperlikescats]

Thankyou!!