SAT Trigonometry: Lesson, Practice Problems & Video Explanations

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By Glyn Caddell, BSME · Author of Digital SAT Math Secrets · Tutoring since 2008 — Updated August 18, 2026

Trigonometry questions test students’ knowledge of sine, cosine, and tangent in a right triangle or in similar triangles. Trigonometry questions appear on approximately 2.0% of the Digital SAT. Trigonometry falls under Geometry and Trigonometry according to the College Board.

Table of Contents

Trigonometry Lesson
Tips
Example
- Video Explanation
- Text Explanation
Practice Problems with Video Explanations
Common Mistakes
FAQs
Related Topics

Trigonometry Lesson for the Digital SAT

The lesson will prepare you for the trigonometry questions that show up on the Digital SAT. This lesson covers what SOH-CAH-TOA is and that sine of an angle is equal to cosine of its complement.

What Do Trigonometry Questions Look Like?

Here are some examples of Trigonometry questions from the Digital SAT.

What is the value of $tan W$ ?
What is the value of $sin (J)$ ?
What is the value of $cos (L)$ ?
What is the value of $tan \dfrac{92\pi}{3}$ ?
In the triangle shown, what is the value of $cos x^o$ ?
Which of the following expressions is equivalent to $(sin 24^o)(cos 66^o)+(cos 24^o)(sin 66^o)$ ?

1. What is SOH-CAH-TOA?

SOH-CAH-TOA is an acronym to help us remember the three basic trigonometric ratios.

SOH stands for Sine = Opposite/Hypotenuse
- $sin\theta = \dfrac{opposite}{hypotenuse}$
CAH stands for Cosine = Adjacent/Hypotenuse
- $cos\theta = \dfrac{adjacent}{hypotenuse}$
TOA stands for Tangent = Opposite/Adjacent
- $tan\theta = \dfrac{opposite}{adjacent}$

Hypotenuse – the hypotenuse of a right triangle is the longest side in a right triangle; it is also always across from the right angle
Opposite side – the opposite side is the side across from (opposite of) the selected angle
Adjacent side – the adjacent side is the side next to the selected angle; it’s the side that isn’t the hypotenuse or the opposite side

Note: The opposite side and adjacent side are always in reference to the angle.

Here are some examples labeled in reference to angle A.

Sine, Cosine, and Tangent are Ratios

If $cosA=\dfrac{2}{5}$ , it doesn’t mean that the length of the adjacent side is 2 and the length of the hypotenuse is 5; it just means that the ratio of length of the adjacent side to the length of the hypotenuse is 2:5.

If two triangles are similar, they have congruent angles and their side lengths are proportionate. Also, sine of one angle will equal sine of the corresponding angle in the other triangle.

For example, If $\triangle ABC$ is similar to $\triangle DEF$ , it means:
$\angle A \cong \angle D$
$\angle B \cong \angle E$
$\angle C \cong \angle F$

The order that the vertices are written is how the vertices match up with each other.

Since the angles are congruent, then
$sinA=sinD$
$sinB=sinE$
$sinC=sinF$

And the same is true for the other trigonometric ratios also, such as $cosA=cosD$ .

2. Sin(A) = Cos(90-A)

$sin x^o = cos(90^o-x^o)$

In other words, sine of an angle is equal to cosine of the complement.

This is an important concept to answer some trigonometry questions quickly and correctly.

Also, a related concept is often tested.

If $sinA^o=cosB^o$ , then $A+B=90$

SAT Tips

Always identify the reference angle in the triangle.
Make sure you label opposite, adjacent, hypotenuse correctly relative to the angle.

Example

In right triangle $ABC$ , angle $C$ is a right angle. If $\overline{AB}=13$ and $\overline{BC}=5$ , what is the value of $sin(A)$ ?

A) $\dfrac{5}{13}$

B) $\dfrac{12}{13}$

C) $\dfrac{5}{12}$

D) $\dfrac{12}{5}$

Video Explanation

Text Explanation

Answer: A

Text Explanation:

Since angle $C$ is a right angle, $\overline{AB}$ is the hypotenuse. For angle $A$ , the opposite side is $\overline{BC}$ . Therefore,

$sin(A)=\dfrac{opposite}{hypotenuse}=\dfrac{BC}{AB}=\dfrac{5}{13}$

The correct answer is A.

Common Mistakes

Two common mistakes students make when answering trigonometry questions are mixing up the trigonometric ratios and mixing up the opposite and adjacent sides in a right triangle.

Mixing Up the Trigonometric Ratios

For some reason, some students say SOH-COH-TOA instead of SOH-CAH-TOA. As a result, they incorrectly set up the cosine ratio as $cosA=\dfrac{opposite}{hypotenuse}$ instead of $cosA=\dfrac{adjacent}{hypotenuse}$ .

Mixing Up the Opposite and Adjacent Sides in the Right Triangle

A common mistake is mixing up the opposite and adjacent sides in a right triangle. Some students get in the habit of always making the bottom (horizontal) side the adjacent side, but that’s not always the adjacent side.

The designation of each side depends on which angle we are applying a trigonometric function to.

Frequently Asked Questions

Here are three frequently asked questions that I get from students when reviewing trigonometry.

Do I Need to Know How to Use Inverse Trigonometry?

No, you do not need to know how to use inverse trigonometry. The questions on the SAT never require you to use inverse trigonometry to find the measure of an angle.

Do I Need to Know Trig Identities?

No, you do not need to know any of the trig identities.

Are Any Formulas Given for Trigonometry on the SAT?

No, there are no formulas specific to trigonometry that are provided on the Digital SAT reference sheet.

The only thing you have to memorize is SOH-CAH-TOA and know how to apply the three associated trigonometric ratios.

There are some formulas and relationships provided that can be used on some trigonometry questions, but the formulas and relationships aren’t directly a part of trigonometry. Specifically, Pythagorean theorem and special right triangles are provided and can sometimes be used in trigonometry questions.