Desmos for the SAT · Technique 3 of 23

Solve Trig Equations (Set Degrees or Radians First)

Desmos defaults to radians. Check the answer choices for a pi, match the mode, then click the crossing.

SolvesTrig equationsDegree modeSine and cosine valuesAngles

Watch the lesson

The whole move worked on one real SAT question, narrated.

0:00 / 0:00

The same question, start to finish: check the choices, switch to Degrees, graph both sides, click the first crossing, then see what Radian mode does to the same two lines.

Desmos assumes radians until you tell it otherwise, and the SAT asks in both: degrees for most angle and triangle questions, radians for arc length, sector area and conversions. Type sin(30) in the default mode and you get -0.988, not 0.5. The answer choices tell you which mode a question wants: plain numbers like 30, 45, 90 mean degrees, and anything with a pi in it means radians. Click the wrench icon (Graph Settings) in the top right and set the mode to match before you type anything.

After that, a trig question is typing. Type the expression exactly as written and read the value Desmos returns. When the question asks for an angle you have not memorized, put each side of the equation on its own line and click where the graphs cross: sin(x) = 0.5 you can recall, sin(x) = 0.35 you cannot, and the graph does not care either way.

Nova

The trap in SAT trig is rarely the trig. It is the calculator's angle mode, and this lesson is about getting it right every time.

Now you try it

The rest of the page takes that move slowly. First how it compares with doing the algebra, then the steps in order, then a real SAT question with a live Desmos calculator to try it in.

The algebra way vs the Desmos way

This technique sidesteps recalling exact values off the unit circle.

The question

2cos(x) = 1, with x measured in degrees

What is the smallest positive value of x: 30, 45, 60 or 90?

The algebra way

Divide both sides by 2: cos(x) = 0.5.
Recall which angle has a cosine of exactly 0.5. Swap it with the angle whose sine is 0.5 and you land on 30, choice A.
If the value is not one you have memorized, there is no by-hand route at all.

The Desmos way

Set the mode to Degrees, then type y = 2cos(x) and y = 1 on two lines.
Click the first crossing and read (60, 1).

The payoff: The graph gives the angle whether or not you have it memorized, and the mode check is the one step that decides if the number on screen is right.

Quick reference

Common values in Degree mode

Angle	sin	cos
0	0	1
30	0.5	0.866
45	0.707	0.707
60	0.866	0.5
90	1	0

Step by step

The whole move, all 4 steps

Check the answer choices for a pi, then set the mode to match: the wrench icon, top right, Radians or Degrees.
Type the expression exactly as the question writes it and read the value Desmos returns.
Match that value against the choices. A value that matches none of them usually means the mode is wrong, so check the wrench again.
If the question asks for an angle instead, put each side of the equation as y = ... on its own line, click inside either equation box to reveal the gray dots, and click the first crossing to read x.

The question

The equation $2\cos(x) = 1$ is given, where x is measured in degrees.

What is the smallest positive value of x, in degrees, that satisfies the equation?

Step 1 of 4

The choices are 30, 45, 60 and 90, plain numbers with no pi, so this question wants degrees. Click the wrench in the top right, pick Degrees, then type the left side as its own line: y = 2cos(x).

In the calculator: y=2cos(x)

Set the mode before typing anything. In Radians the same two lines first cross at about 1.05, which is not one of the choices.

Syntax: Type sin, cos, or tan and Desmos formats it as a function. The angle mode lives in the wrench menu, not in the expression: typing deg after a number does nothing.

Now try it on a real SAT question

Desmos wins. By hand this means subtracting full turns from $\frac{565\pi}{6}$ until what is left sits between 0 and $2\pi$ , which is a long division you have no way to check. Desmos evaluates it directly, as long as the mode is right, and the mode is the entire question.

Consider the expression $\cos\left(\frac{565\pi}{6}\right)$ .

What is the value of the given expression?

Pick an answer to get instant coaching from Nova.

Stuck?

Your turnstarts empty

Set this question up yourself, then read the answer straight off the graph.

The Desmos trap: when to close the calculator

If the angle is one you know cold (0, 30, 45, 60, or 90 degrees), recall the value. Graphing it is slower.
For a right-triangle SOHCAHTOA problem, Desmos will not draw the triangle for you. Set up the sine, cosine, or tangent ratio yourself, then let Desmos do the arithmetic.
Set the mode before anything else, and let the answer choices pick it: plain numbers mean degrees, a pi means radians. The wrong one hands you a confident wrong number with nothing on screen to warn you.

All Desmos techniques

Put this move into real practice

"Solve Trig Equations (Set Degrees or Radians First)" shows up all over the real SAT. SAT Prep Quest drills the skill at your level, so reaching for it becomes automatic by test day.

Practice free

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