August 7, 2026
Is the Law of Cosines on the SAT? Key Facts
Is the law of cosines on the SAT? Learn whether it is tested, what trigonometry the SAT covers instead, the formula, and how the ACT differs.
The direct answer: the law of cosines is not a tested SAT® Math skill on the current digital test. You should expect zero questions that require the formula, which means it represents 0 percent of SAT® Math as a required topic. The SAT® tests right-triangle trigonometry and selected unit-circle relationships, not solving general, non-right triangles. This article explains the test status, the formula, how it compares with the ACT, when it is taught, and the calculator rules.
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Law of Cosines at a Glance
| Question | Answer |
|---|---|
| Is the law of cosines tested on the SAT®? | No, not as a required SAT® Math formula or skill. |
| Separate official category? | No. It falls outside the stated trigonometry skills. |
| How many questions cover it? | Zero expected questions that require it. |
| Percentage of SAT® Math? | 0 percent as a required skill. |
| On the reference sheet? | No. The Pythagorean theorem is listed, not this law. |
| Calculator allowed? | Yes, throughout the entire Math section. |
| Usually taught in? | Grade 10 or 11 (geometry, Algebra 2, or precalculus). |
| On the ACT? | Yes. The ACT includes law of sines and cosines. |
Is the Law of Cosines Tested on the SAT®?
No. Current SAT® Math specifications describe trigonometry through right triangles and selected unit-circle relationships. They do not list solving general, non-right triangles with the law of cosines. College Board's own Geometry and Trigonometry page lists the tested areas as area and volume, lines angles and triangles, right triangles and trigonometry, and circles (College Board Geometry and Trigonometry). The Math specifications add that students solve problems "using the Pythagorean theorem, right triangle and unit circle trigonometry, and properties of special right triangles" (College Board Math Specifications).
The word "cosine" can mean two different things, and this is where confusion starts:
- The ordinary cosine ratio in a right triangle: cos(θ) = adjacent / hypotenuse.
- The law of cosines for a general triangle: c² = a² + b² − 2ab·cos(C).
The first belongs in SAT® Math. The second is a broader relationship that is not part of the test's stated skill inventory. Seeing "cosine" in prep material does not mean the law of cosines is tested.
What the SAT® Tests Instead
The expected number of law of cosines questions is zero per test. That gives 0 out of 44 Math questions, or 0 percent, when counting questions that require the formula.
Do not confuse this with the weight of the full Geometry and Trigonometry domain. The digital SAT® Math section has 44 questions, and about 5 to 7 fall within Geometry and Trigonometry. College Board places that domain at roughly 15 percent of SAT® Math (College Board Math Specifications). That domain is broader than trigonometry alone and combines several skills, so students should not assume every listed triangle or circle skill appears in a dedicated question on a given form.
The SAT® reference information includes the Pythagorean theorem and common geometry formulas, but it does not list the law of cosines. A calculator is permitted throughout the entire digital SAT® Math section, including every geometry and trigonometry question. A question stated in degrees requires degree mode; a radian expression requires radian mode. The provision of a calculator does not change the content scope.
The Law of Cosines Formula
The standard law of cosines formula is:
c² = a² + b² − 2ab·cos(C)
Here, sides a, b, and c are opposite angles A, B, and C. The formula relates all three side lengths to the cosine of one angle. Equivalent versions exist for the other two sides.
The law of cosines is also a generalisation of the Pythagorean theorem. If C = 90°, then cos(90°) = 0, so the final term disappears and you get c² = a² + b². That connection explains why the formulas look similar, but it does not make the full law of cosines an SAT® requirement. The Pythagorean theorem is tested and appears on the SAT® reference sheet, while the law of cosines does not. Third party prep guides agree: Magoosh notes plainly that "the law of cosines, and just about everything else from trigonometry, is not tested on the SAT®" (Magoosh SAT® triangles).
ACT Comparison and When It Is Taught
The ACT Math content scope includes applying the laws of sines and cosines to questions involving non-right triangles. This is an important difference between the two exams. The ACT covers a broader range of trigonometry than the SAT®, including general-triangle relationships, and its Math assessment draws from material typically taught through the beginning of grade 12 (Piqosity digital SAT® content).
| Trigonometry feature | SAT® | ACT |
|---|---|---|
| Right-triangle sine, cosine, tangent | Yes | Yes |
| Law of cosines | Not an explicitly tested skill | Yes |
| Law of sines | Not an explicitly tested skill | Yes |
| Calculator permitted in Math | Yes | Yes |
The law of cosines is generally taught in high school geometry, Algebra 2, trigonometry, or precalculus, often around grades 10 or 11. Some students study it earlier or later. Completing a geometry class does not guarantee every student has seen the formula. Grade level and SAT® coverage are separate questions: the SAT® emphasizes selected mathematics considered important for college readiness, not a complete high school syllabus.
Common Misconceptions
- "There will definitely be a law of cosines question." No individual formula is guaranteed; only broader domain ranges are published.
- "The reference sheet gives the law of cosines." It does not, though it provides the related Pythagorean theorem.
- "A calculator removes the need to understand it." A calculator evaluates expressions but cannot decide whether a question requires this relationship.
- "ACT and SAT® test the same trigonometry." The ACT goes further and includes the general-triangle laws.
- "Right-triangle trig is the same as the law of cosines." They are related but distinct; only right-triangle trig is in scope.
Frequently Asked Questions
Is the law of cosines on the SAT®?
No. It is not an explicitly tested SAT® Math skill under the current digital specifications (College Board Geometry and Trigonometry).
Is ordinary cosine tested even though the law of cosines is not?
Yes. Right-triangle sine, cosine, and tangent ratios are within the SAT® Math scope.
Does the SAT® reference sheet include the law of cosines formula?
No. It includes the Pythagorean theorem and other common geometry relationships, but not the law of cosines.
Should students taking both the SAT® and ACT memorize the law of cosines?
If you are also taking the ACT, yes, because the ACT tests general-triangle laws. For the SAT® alone, it is not required.
Can an approved calculator apply the law of cosines automatically?
A calculator can evaluate cosine expressions, but it cannot decide whether a question requires the law of cosines. That judgment comes from understanding the problem.
What should SAT® students prioritize instead?
The Pythagorean theorem, special right triangles, similarity, angle relationships, and right-triangle trig ratios.
About the author
Priya S. is a perfect-scoring SAT verbal specialist and former test-prep lead with over 12 years coaching the Reading & Writing section, including through the shift to the digital adaptive format. Her focus is the digital SAT Reading & Writing module, teaching students to read for the test-writer's intent and apply grammar rules mechanically.