Desmos Degrees or Radians? How to Tell on SAT/ACT Trig Questions
Desmos defaults to radians. Most SAT and ACT trigonometry questions are written in degrees. That small mismatch is one of the most common ways students lose points on an otherwise correct approach—the math is right, but the calculator quietly gives back the wrong number.
Here’s how to know which mode you need, and how to check your work either way.
Watch: applying this to two real SAT/ACT problems (3 min)
Show transcript
In this video, we’re going to talk about how to decide whether to put Desmos in radians or degrees.
For the first problem, we’re deciding whether to switch Desmos to degrees, so we start by looking for the degree symbol—that little circle—or the word “degrees.” This problem doesn’t have a degree symbol anywhere, but it does use the word “degrees.” That’s our signal to put Desmos in degrees.
Now let’s plot it. The problem says cos(Q) = sin(R), so we’re looking for the point where these two functions intersect. Plotting both, we can see they intersect—but first, let’s check the mode. It’s still in radians, so we need to switch to degrees before we trust the result.
After switching to degrees, there’s only one relevant intersection point, and its x-value is 5. So the answer is 5.
Let’s try another problem. Again, we look for the word “degrees” or the degree symbol—and here, the degree symbol shows up several times. Let’s plug this into Desmos.
This time we’re solving for x using arcsine, the inverse of sine. Setting x1 = arcsin(5/8) gives us 38.68. Now we can use x1 to find cos(90 − x1).
Before trusting that result, we check the mode again—yes, we’re in degrees—so our answer is 0.625.
That’s how you choose between radians and degrees in Desmos.
Why This Happens
Every trig function—sin, cos, tan, and their inverses—needs to know what unit an angle is measured in before it can calculate anything. Desmos assumes radians unless you tell it otherwise.
Example
In radian mode, this evaluates 30 radians—a huge angle that travels many full rotations around the circle—not 30 degrees. The result won’t match what the SAT is asking for.
Spotting a Degree Problem
Right-triangle trig questions on the SAT and ACT are almost always in degrees. Look for the degree symbol directly on the angle, or the word degrees in the setup.
Example
The ° symbol on x° and 90° is the signal. If you check this numerically in Desmos, switch to degree mode first: tap the wrench icon, then set Angle to Degrees.
Spotting a Radian Problem
Circle questions that involve arc length, or any problem that gives you an angle as a multiple of π, are almost always in radians—Desmos’s default mode.
Example
There’s no degree symbol here, and the angle is written in terms of π. Leave Desmos in radian mode for this one. Switching to degrees would give a completely different, incorrect result.
Checking a Trig Equation in Desmos
Some problems hide an angle-solving equation inside an algebra setup. These are worth checking graphically, but only after the mode is set correctly.
Example
Since the cosine and sine of complementary angles are equal, ∠Q and ∠R must sum to 90°:
To confirm graphically, set Desmos to degree mode, then graph y₁ = cos(x + 61) and y₂ = sin(4x + 4). The relevant intersection point should land at x = 5.
Quick Reference
| Angle looks like... | Use this mode |
|---|---|
| 30°, x°, “measures in degrees” | Degrees |
| π/3, 2π, “radians” | Radians |
| No units given, but the problem is a right-triangle ratio | Degrees (default for SAT/ACT triangle trig) |
| No units given, but the problem involves arc length or a unit circle with π | Radians |
Mini Tips
- Check your calculator’s angle mode before you graph—not after you get a strange answer.
- The wrench icon in the top right of Desmos controls angle mode.
- When in doubt, solve the problem by hand first using an identity or ratio, then use Desmos only to double-check the number.
Want help applying this to real test questions?
Catching the degree-versus-radian switch is one of those small habits that saves real points once it’s automatic. That part gets much easier with targeted practice and feedback.