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# Tip #35 to Get a Top ACT Math Score

By Brian Leaf
McGraw-Hill Professional
Updated on Sep 7, 2011

Half of the trig questions on the ACT are just SohCahToa, which you've now mastered. Many kids think that the rest of the trig questions are way beyond them, that you can only get them if you've had a full-year trig course. If you've had a trig course, that's great, and these questions will be especially easy for you. If not, the exciting news is that almost every trig question can be done with "Use the Answers" or "Make It Real"! You'll see examples of this when we review the Pretest question and in the drills.

When the ACT wants you to use a specific trig concept, such as the law of sines or law of cosines, they will explain it in the question, and you just have to follow the directions. These are great; they give you the equation, and you just follow the directions. You'll see this also in the drills.

Lastly, occasionally the ACT has a question about the reciprocals of sin, cos, and tan, which are

Let's look at this question:

Solution: θ is just the symbol that people use for an angle when it's unknown. (The symbol is called theta.) Therefore, "what is the value of θ" means "what is the angle measure?" You probably could have guessed that anyway, since the question tells you that θ is between 0 and 360. Another example of "Don't get intimidated!" Just go with it, make an assumption on the ACT, and you'll probably be correct. They set it up that way. This is a great example of a Beyond SohCahToa question where you really don't need any trig. You just need to "Use the Answers"! Using your calculator, try each choice for θ and see which one gives you sin θ = –1. Choice D is correct, because sin 270 = –1. If using the "sin" button is new for you, practice it right now. It's easy. Just hit "sin" and type "270" and hit Enter and you'll get an answer of –1.

### Hard

1. What are the values of θ, between 0° and 360°, when tan θ = 1 ?
1. 45°, 135°, 225°, and 315°
2. 45° and 135° only
3. 45° and 225° only
4. 45° and 315° only
5. 135° and 315° only
2. Which of the following expressions gives the perimeter of the triangle shown below, with measurements as marked?
3. (Note: The law of sines states that the ratios between the length of the side opposite any angle and the sine of that angle are equal for all interior angles in the same triangle.)

4. Which of the following equations reflects the graph shown below?
1. y = sin x
2. y = 5 sin (x - 2)
3. y = 2 cos x - 2
4. y = cos (x - 2) - 2
5. y = 2 tan x - 5
5. If b, c, and d represent positive real numbers, what is the minimum value of the function f(x) = sin b(x - c) - d ?
1. 0
2. 1
3. -b
1. d + c
2. -1 - d

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