Physics - Solving Trig Functions without a Calculator

The good news is that you don’t have to be able to do this on actual MCAT questions. All you would need to be able to do at the very most on a problem is to estimate where your trig function value will fall with relation to the five angles that you know. (You should know the cos and sin values for 0, 30, 45, 60, and 90 degrees; if you don’t, memorize them NOW.) That’ll be enough to choose the answer using process of elimination.

Here’s the general approach to MCAT questions that ask for an angle as an answer. First, the only angles you need to know anything about are 30, 45, and 60 degrees (plus things like 0 and 90, plus equivalent angles like 135 [which is the same as 45]). Moreover, you don’t need to know them with any precision: on MCAT physics questions, one significant figure is plenty. This means that for 30 degrees, sine is 0.5 and cosine is 0.9; for 60 degrees these two are reversed, and for 45 degrees the sine and cosine are each 0.7. (Warning: MCAT chemistry questions sometimes do require more than one significant figure, but there’s no trig needed for them.)

How, then, do you answer questions whose answers are other than these? Glad you asked. The rule is this: angular answers to MCAT problems can only be angles you know about, plus angles that are actually discussed in the question or the passage, unless only one of the four answer choices is possible. In other words, any answer choice that is an angle that you don’t know anything about (i.e., haven’t memorized the sine and cosine of) and that isn’t listed in the passage, cannot be the answer unless all other choices are obviously wrong. You can estimate which one is correct by using the angles that you know. For example, if you were asked for sin 15 degrees, you know it must be greater than sin 0 (which is 0) and less than sin 30 (which is 0.5). Only one of your four answer choices will be between 0 and 0.5, and that is the correct answer.

Note about tangent: I don’t know when you’d need tangent on the MCAT. To sum, you only need to know the following angles for sine and cosine:

• cos (0) = 1; sin(0) = 0
• cos(30) = 0.9; sin(30) = 0.5
• cos(45) = 0.7; sin(45) = 0.7
• cos(60) = 0.5; sin(60) = 0.9
• cos(90) = 0; sin(90) = 1

Any other angle, you will be given the trig functions for, or you will only have to see that the function is bigger/smaller than one of the angles listed above. The mnemonic for trig functions is SOH CAH TOA: sine = opposite over hypotenuse, cosine = adjacent over hypotenuse, tangent = opposite over adjacent.