Honors pre-calc anybody? (or trig).
also, do a great job explaining how you got the answer and why.

(i'll give brainliest to anybody who can explain how to do any other problems like this in general).

  sec(θ) = -5/2

Step-by-step explanation:

It can be helpful to draw a triangle with sides that produce the given ratio. See the attachment. Then the third side of the triangle can be found using the Pythagorean theorem, if necessary. Finally, the ratio for the desired trig function can be determined.

  sec = hypotenuse/adjacent

  sec(θ) = 5/-2 = -5/2

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If you don't want to do that, or if you have various trig identities memorized, you can use the appropriate trig identity.

  sin² + cos² = 1

so ...

  sec² = 1/cos² = 1/(1 -sin²)

  sec = 1/√(1 -sin²)

Since the tangent is positive, this is a third-quadrant angle. The secant will be negative.

  sec(θ) = -1/√(1 -(21/25)) = -√(25/4) . . . . . filling in the given value for sin(θ)

  sec(θ) = -5/2

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!