Tip #35 to Get a Top ACT Math Score

Answers

1. C Awesome "Use the Answers" question! Try each answer choice, and use the process of elimination until you find the 1 choice that has values that all work. Choice C is correct since both 45 and 225 yield 1 when plugged in for #&952; in the expression tan #&952;. If you've studied trig, you could also do this question the "math class way." Since tan means "opposite over adjacent," tan #&952; = 1 when opposite = adjacent, and therefore sin = cos. So what are the values for #&952; where sin = cos? Sin could equal cos when #&952; is between 0 and 90 or between 180 and 270, because in these regions sin and cos are either both positive or both negative. Use the process of elimination, and only choice C has answers in these two regions.
2. F Follow the directions given for the law of sines. The ratio of a side and the sin of its opposite angle is equal for all sides. So Perimeter equals the sum of the sides of the triangle, and we already know two of the sides. We can use that ratio to solve for x, the third side. So since we can cross-multiply to get (x)(sin 74) = (32)(sin 52), and divide both sides by sin 74 to get Therefore, the perimeter equals
3. D Notice that all of these are "hards." You would only see this Beyond SohCahToa stuff as hards. You can "Use the Answers" here. Graph each answer choice on your calculator, and find the one that matches the graph shown in the question. You'll notice, when you graph these, that they don't make the curved line like in the picture; that's your tipoff that you need to change your calculator to radians mode. That's the only curveball for this particular type of question. You need to change the mode on your calculator to radians, and you have to remember to switch it back when you're done. Just ask your math teacher to show you this if you've never done it before. Radians are just another way (besides degrees) to measure an angle. Once you know how to do this on your calculator, choice D matches perfectly.

If you've studied trig, you could also do this question the "math class way." The graph shown has been shifted from its usual position. When a graph has been shifted, we can use the equation y = a cos b(x – c) – d, where a tells the altitude of the curve (how high up and down it reaches), b/(2π) tells the period (the length of one repeat), c tells how far left or right the graph was moved from the origin, and d tells how far up or down the graph was moved from the origin. The graph in the question has been shifted down and to the right from the ordinary cos graph. So we want a cos graph with a right and down shift, represented by the c and d. So answer choice D is correct. It is the only one with a number for c and d in the equation y = a cos b(x – c) – d.

4. K This question is crazy theoretical, so you can "Make It Real." Just choose positive numbers for b, c, and d and graph the equation on your calculator. Then find the minimum value (the lowest point) of the graph. You'll notice when you graph these that they don't make the usual trig curved graph like the diagram in question 3; that's your tipoff that you need to change your calculator to radians mode. That's the only curveball for this particular type of question. You need to change the mode on your calculator to radians, and you have to remember to switch it back when you're done. Just ask your math teacher to show you this if you've never done it before. Radians are just another way (besides degrees) to measure an angle, and once you know how to do this on your calculator, it's easy.

To "Make It Real," let's say b = 2, c = 3, and d = 4; then the graph shows a minimum value of –5. Using the numbers we choose for b, c, and d in the answer choices, we need the choice that also yields –5. Choice K works, since –1 – 4 = –5.

If you've studied trig, you could also do this question the "math class way." In the equation y = a cos b(x – c) – d, the c tells how far left or right the graph was moved from the origin, and d tells how far up or down the graph was moved from the origin. So this graph will always reach a minimum of –1 – d, since it's normal minimum is –1 and it has been shifted down d units, giving a new minimum of –1 – d.

Go to: Tip #36