SAT Trigonometry: How to Use SOHCAHTOA
Trigonometry isn’t a primary focus on the new SAT. However, according to the CollegeBoard, around six of the 58 questions included on the Math section of the test do deal with Additional Topics in Math, one of which is trigonometry. Referring to the branch of math related to the relationship between angles and triangle side lengths, trigonometry involves working with right triangles to identify missing side lengths and angle measurements.
Although the presence of trigonometry concepts on the SAT can cause anxiety among test takers, the truth is that answering these questions correctly is just a matter of knowing which tools to use. Most of the trig questions on the SAT ask students to use sine, cosine, and tangent to solve problems involving right triangles. Read on to learn more about the questions you can expect to encounter on the SAT Math, as well as how to use the acronym SOHCAHTOA to boost your score.
What Trigonometry Concepts Are on the SAT?
Students taking the SAT can expect to encounter two main types of trigonometry questions. If you take the time to study both question types, you’ll have a good chance of succeeding on this part of the test.
The first question variety requires students to use the measures of a triangle’s sides to find the sine, cosine, or tangent of an angle. For the second question type, students will be asked to determine an angle’s sine, cosine, or tangent using the sine, cosine, or tangent of another angle that’s been provided. In both cases, students can use the acronym SOHCAHTOA to ensure that they answer the questions correctly.
What Is SOHCAHTOA?
Memorizing math formulas can be tedious and stressful; what if you forget a key component and use the wrong information to solve problems? SOHCAHTOA is an acronym that exists to help trigonometry students remember how to solve problems related to right triangles.
The three-letter groupings in SOHCAHTOA stands for the following:
SOH: Sine equals Opposite over Hypotenuse.
CAH: Cosine equals Adjacent over Hypotenuse.
TOA: Tangent equals Opposite over Adjacent.
Here, the terms Opposite, Adjacent, and Hypotenuse all refer to the measurement of sides of a right triangle. It’s worth noting that the hypotenuse is the side located opposite the right angle. It’s also the longest side in the triangle. The opposite side refers to the one located opposite the angle with an unknown measurement. Finally, the adjacent side is the one touching the unknown angle.
Solving SAT Trigonometry Questions
The first type of SAT trigonometry question asks students to solve for an angle’s sine, cosine, or tangent. For example, in triangle ABC, where B is the right angle, the question may include the length of the hypotenuse (4) and side BC (3) and ask students to determine the cosine of angle C.
For some problems, the SAT will provide you with a diagram, and in other cases you’ll have to draw one yourself. If you have to draw your own triangle, start by filling in the information provided. In this case, you would fill in the length of the hypotenuse and side BC. Then assess what information you need to find and choose the correct formula for solving the problem.
For example, if you’re asked to find the cosine of angle C, you can do so with the following equation:
Cos C = The length of the adjacent side of the triangle (BC) / the length of the hypotenuse
So, the cosine of C is equal to 3/4.
When solving the second question type, students will use the sine, cosine, or tangent of an acute angle to determine the sine, cosine, or tangent of another angle. For example, a problem involving a triangle ABC, where B is the right angle, may provide the cosine of angle C and ask you to come up with the sine of angle A.
To solve this problem, start by using the cosine formula to determine what information should go where in your diagram. So, if the cosine of angle C is 3/4, then the measure of the adjacent side (BC) is 3 and the measure of the hypotenuse is 4.
You can then calculate the sine of angle A using the following formula:
Sine A = length of the side opposite the angle (BC) / length of the hypotenuse.
In other words, Sine A is equal to 3/4.
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