SAT Trigonometry: What’s Tested, with 6 Worked Examples

Sriram Venkataraman

03/11/2026

10 min read

SAT trigonometry is a small, predictable slice of the Math section. It sits inside College Board’s Geometry and Trigonometry domain, which accounts for about 15% of the section, or 5–7 of the 44 Math questions, and those questions are shared with area, volume, angles and circles. So on test day expect only a handful of trig questions, but they reward a few facts learned well.

This guide sets out exactly which trig skills College Board lists for the SAT, what the on-screen reference sheet gives you (and what it leaves out), and six worked examples. Every example was written by Galvanize for this page, so none of them is a College Board question.

How much trigonometry is on the SAT?

The Math section has 44 questions in 70 minutes, split into two modules. College Board’s Assessment Framework for the Digital SAT Suite (version 4, September 2026, checked 31 Oct 2026) gives the Geometry and Trigonometry domain about 15% of the section, which is 5–7 questions. That domain has four skill areas, and only two of them involve trig:

College Board does not publish a separate count for trig questions, so any figure you see for “trig questions per test” is an estimate. What is certain is that trig competes for a share of just 5–7 questions. That is why it is worth learning the short list below thoroughly rather than studying trigonometry as a whole school subject.

Which trigonometry topics does the SAT test?

The detailed skill tables in Appendix B of the Assessment Framework list these trig skills for the SAT:

• Right triangle trigonometry. Solve problems with the Pythagorean theorem, the properties of special right triangles and the sine, cosine and tangent ratios.
• Trig values from similar triangles. Use similarity to work out sine, cosine and tangent. Every right triangle with the same acute angle has the same ratios, however big it is.
• Complementary angles. Solve problems using the relationship between the sine and cosine of complementary angles: sin(x°) = cos(90° − x°).
• Radians. Convert between degrees and radians, and solve problems using radian measure.
• The unit circle. Solve problems using trigonometric ratios in the unit circle.

The framework marks calculating with sine, cosine and tangent, radian measure and unit-circle trigonometry as SAT-only skills, not tested on the PSAT exams, and says questions in this domain range from easy to very hard.

Just as useful is what is missing. The list does not mention the law of sines or the law of cosines, graphs of sine and cosine, trig identities beyond the complementary-angle rule, inverse trig functions, or secant, cosecant and cotangent. If a prep book spends chapters on those, it is teaching beyond what College Board lists for the SAT.

What does the SAT reference sheet give you for trig?

On the Math section you can open a reference sheet of common formulas in Bluebook. The version reproduced in Appendix D of the Assessment Framework includes these items relevant to trig:

The conversion and the arc-length formula both follow from the sheet’s “360 degrees = 2π radians” line, but working them out on the clock costs time. Memorise the right-hand column so that you only use the sheet as a check.

What do you need to know about right-triangle trig?

For an acute angle in a right triangle, name the sides from that angle’s point of view: the opposite side faces it, the adjacent side touches it, and the hypotenuse faces the right angle.

Two facts make many questions quick. First, sine and cosine of an acute angle are always between 0 and 1, because the hypotenuse is the longest side. Second, the two acute angles of a right triangle add up to 90°, so the side opposite one angle is adjacent to the other. That is why the sine of one acute angle equals the cosine of the other.

How do radians and the unit circle work on the SAT?

A radian is the angle that cuts off an arc equal in length to the radius. A full turn is 2π radians, so π radians = 180°. To convert degrees to radians, multiply by π/180; to convert radians to degrees, multiply by 180/π.

The unit circle is the circle of radius 1 centred at the origin. For an angle θ measured anticlockwise from the positive x-axis, the point where the angle’s side meets the circle is (cos θ, sin θ). These are the values worth knowing by heart:

For angles past 90°, find the reference angle (the acute angle to the x-axis) and then fix the sign by quadrant: cosine is negative on the left half of the circle and sine is negative on the bottom half.

A calculator tip: the built-in Desmos calculator is available for the whole Math section, according to the Assessment Framework. Before you type a trig value, check whether it is set to degrees or radians. tan(35) in radian mode gives about 0.474, while tan 35° is about 0.700. Our guide to the Desmos SAT calculator covers the settings.

SAT trigonometry examples with step-by-step solutions

Try each one before reading the solution. With 70 minutes for 44 questions, you have about 95 seconds per Math question on average.

Example 1: Right-triangle ratios

In right triangle PQR, angle R is the right angle, PQ = 26 and QR = 10. What is tan P?

• PQ is opposite the right angle, so it is the hypotenuse.
• Find the missing leg: PR² = 26² − 10² = 676 − 100 = 576, so PR = 24. (This is the 5-12-13 triple doubled.)
• From angle P, the opposite side is QR = 10 and the adjacent side is PR = 24.
• tan P = 10/24 = 5/12.

The trap: 12/5, which is tan Q. Label opposite and adjacent from the angle the question names.

Example 2: Sine and cosine of complementary angles

The angles (2k + 8)° and (3k + 7)° are both acute, and sin((2k + 8)°) = cos((3k + 7)°). What is the value of k?

• For acute angles, sin A = cos B exactly when A + B = 90°.
• (2k + 8) + (3k + 7) = 90, so 5k + 15 = 90 and k = 15.
• Check: the angles are 38° and 52°, which add up to 90°.
• Answer: k = 15.

The trap: setting the two angles equal to each other. Equal sine and cosine values point to complementary angles, not equal ones.

Example 3: A 30°-60°-90° triangle

A straight ramp 12 metres long rises from level ground at an angle of 30°. What is the horizontal distance the ramp covers, in metres?

• The ramp, the ground and the vertical rise form a 30°-60°-90° triangle with the ramp as the hypotenuse.
• From the reference sheet, the sides are x, x√3 and 2x. The hypotenuse 2x = 12, so x = 6.
• The rise is opposite the 30° angle, so it is the short side, 6 m. The horizontal distance is the longer leg, x√3.
• Answer: 6√3 metres, about 10.39 m.

The trap: giving 6, the height. The side opposite the smallest angle is always the shortest side.

Example 4: Radians and arc length

A circle has radius 9. A central angle of 2π/3 radians cuts off an arc. What is the length of the arc?

• With the angle in radians, arc length = radius × angle: s = 9 × 2π/3 = 6π.
• Check in degrees: 2π/3 × 180/π = 120°, which is a third of the circle. The circumference is 2π × 9 = 18π, and a third of 18π is 6π.
• Answer: 6π, about 18.85.

The fraction-of-the-circle check works for any arc or sector question, and it uses only facts that are on the reference sheet.

Example 5: The unit circle

Point P lies on the unit circle centred at the origin O. Segment OP makes an angle of 4π/3 radians, measured anticlockwise, with the positive x-axis. What is the y-coordinate of P?

• Convert: 4π/3 × 180/π = 240°, which is in the third quadrant (bottom left).
• The reference angle is 240° − 180° = 60°, and sin 60° = √3/2.
• In the third quadrant both coordinates are negative, so P = (−1/2, −√3/2).
• Answer: −√3/2, about −0.866.

The trap: dropping the minus sign. Sketch the angle first; the sketch tells you the sign before you calculate anything.

Example 6: Trig values from similar triangles

In right triangle ABC, angle C is the right angle, tan B = 8/15 and the hypotenuse AB = 51. What is the length of the shorter leg?

• tan B = 8/15 means the legs are in the ratio 8 : 15, so the triangle is similar to an 8-15-17 triangle (8² + 15² = 64 + 225 = 289 = 17²).
• Scale factor: 51 ÷ 17 = 3.
• The legs are 8 × 3 = 24 and 15 × 3 = 45.
• Answer: 24.

Scaling a triangle changes the side lengths but not the angles, so the trig ratios stay the same. Here sin B = 24/51 = 8/17, the same as in the small triangle.

What mistakes cost the most marks on SAT trig questions?

• Naming sides from the wrong angle. Opposite and adjacent swap when you switch angles (Example 1).
• Calculator in the wrong mode. A degree question worked in radian mode, or the other way round, gives a confident wrong answer.
• Setting complementary angles equal. sin A = cos B means A + B = 90° (Example 2).
• Mixing up the special-triangle sides. In a 30°-60°-90° triangle the hypotenuse is 2x, and x√3 is the longer leg (Example 3).
• Losing the sign on the unit circle. Past 90°, decide the quadrant before you write the value (Example 5).

How should you practise SAT trigonometry?

Because trig is a small share of the test, a short, focused plan beats a long one.

• Learn the five skills above and the “not on the reference sheet” column until you can write them from memory.
• Work mixed geometry sets on our SAT math practice page, and read the trig section of our SAT geometry guide for the triangle and circle questions that sit alongside trig.
• See where trig fits in the wider section in the ultimate SAT math study guide and our guide to the four SAT Math domains.
• Then take a timed SAT practice test and convert your result with the SAT score calculator.

Not sure whether trig or another Math domain is costing you points? Take the free SAT diagnostic test to see your weak areas by domain before you plan your study time. If you are applying to US universities, our admission counselling team can help you set a target SAT score for your college list.