Choose all answers that are correct.

Step-by-step explanation:

In quadrant IV, the tangent is negative, so the first answer choice cannot be correct.

The triangle involved is a 3-4-5 triangle, so the second answer choice cannot be correct.

The cosecant can be found several ways. One is to find the sine of the angle (-4/5 — compare to answer choice 2), then invert it. (csc(θ) = 1/sin(θ)) Here that means csc(θ) = 1/(-4/5) = -5/4, in agreement with the third answer choice.

cos(θ) = 1/sec(θ) = 1/(5/3) = 3/5, in agreement with the fourth answer choice.

Comment on cosecant

You know from SOH CAH TOA that ...

  Cos = Adjacent/Hypotenuse

Then Sec = 1/Cos = Hypotenuse/Adjacent. This can help you draw the triangle, which you quickly realize is a 3-4-5 right triangle. If not, you can use the Pythagorean theorem to find the opposite side length as ...

  √(5²-3²) = √16 = 4

Remember the triangle is being drawn in the 4th quadrant, so the side opposite the angle will be negative.

Of course, Csc = 1/Sin = Hypotenuse/Opposite, so is 5/(-4) = -5/4.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1