Answer by formula please ​

Step-by-step explanation:

I honestly have no idea what you mean by answer by formula, but I'm going to give it my best. I began by squaring both sides to get:

(a² - b²) tan²θ = b² and then distributed to get:

a² tan²θ - b² tan²θ = b² and then got the b terms on the side to get:

a² tan²θ = b² + b² tan²θ and then changed the tans to sin/cos to get:

and isolated the sin-squared on the left to get:

and distributed to get:

****** and factored the right side to get:

and utilized a trig Pythagorean identity to get:

and then solved for sinθ in the following way:

so

This, along with the *** expression above will be important. I'm picking up at the *** to solve for cosθ:

and get the cos²θ alone on the right by subtracting to get:

and divide by b² to get:

and factor on the left to get:

and take the square root of both sides to get:

and simplify to get:

and go back to the identity we found for sinθ and sub it in to get:

and simplifying a bit gives us:

That's my spin on things....not sure if it's what you were looking for. If not.....YIKES

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.