SAT Trig Expressions on Desmos: Check Sin and Cos

To check an SAT trig expression on Desmos, set the angle mode to match the question, store a test angle in a letter such as a, and type the expression and each answer choice on their own lines. The choice whose value matches the expression is the equivalent one. Two identities cover most of these questions: sin(x°) = cos((90 - x)°), and sin²(x) + cos²(x) = 1.

You can follow along on the College Board version of the calculator on our Desmos on the SAT page. Bluebook, the app you take the SAT in, has Desmos built in, and College Board allows a calculator on the whole Math section. Below, you watch one SAT-style expression checked step by step, finish a second one with help, and then solve two on your own.

Three checks before you type

1. Match the angle mode. If the question shows a degree sign, use degrees. If it uses π or says radians, use radians. To test the mode, type sin(30). Degree mode gives 0.5, and radian mode gives about -0.988. When we opened the College Board graphing calculator on desmos.com on September 26, 2026, it started in radians. We have not confirmed which mode Bluebook starts in, so run the sin(30) test on test day too, and switch the mode in the graph settings if you need to.
2. Store test values in letters like a, b or t. Desmos treats x and y as graph variables, so typing x = 37 draws a vertical line and stores nothing. In our check, typing θ = arctan(3/4) returned an error, because Desmos saves θ for polar graphs. A line like a = 37 stores the number, and every later line can use it.
3. Compare values, then change the test value once. Type the expression on one line and each answer choice on its own line. The equivalent choice gives the same value. Then change the stored angle and look again, because two different expressions can agree at one angle.

The identities behind these questions

The first two rows are written in degrees. In radians, the complement of x is π/2 - x. You can skip the derivations. The Desmos check below tells you which identity a question is built on.

Example 1, worked for you: a cofunction question

Which expression is equivalent to cos((90 - x)°) for all values of x?

A) sin(x°)
B) cos(x°)
C) -sin(x°)
D) 1 - cos(x°)

SAT-style question written by TTA.

The question uses degree signs, so I set degree mode and type sin(30) to make sure it reads 0.5. Then I store a test angle and type the expression and the four choices:

Line 1: a = 37
Line 2: cos(90 - a) shows 0.6018
Line 3: sin(a) shows 0.6018
Line 4: cos(a) shows 0.7986
Line 5: -sin(a) shows -0.6018
Line 6: 1 - cos(a) shows 0.2014

I picked 37 on purpose. At 45, sin and cos give the same value, so choices A and B would look identical. At 37 only line 3 matches line 2.

One match could be luck, so I change line 1 to a = 71. Now cos(90 - a) and sin(a) both show 0.9455, and cos(a) shows 0.3256. Choice A matches at both angles.

By hand, the two acute angles of a right triangle add to 90°. The side opposite one angle is adjacent to the other, so the cosine of the complement equals the sine of the angle. The answer is A.

Example 2, guided: from tan to sin + cos

If tan(b°) = 3/4 and 0 < b < 90, what is the value of sin(b°) + cos(b°)?

SAT-style question written by TTA.

Line 1: b = arctan(3/4). In degree mode, Desmos shows about 36.87. You don't need that number, because b now holds it.

Line 2 is yours. Type the expression the question asks for, using b, and read the value.

Check your answer: sin(b) + cos(b) shows 1.4, which is 7/5. By hand, tan = opposite/adjacent = 3/4 gives a 3-4-5 right triangle, so sin(b°) = 3/5, cos(b°) = 4/5, and the sum is 7/5. If the choices are fractions, pick 7/5. The same two lines handle a ratio like 5/7, which has no whole-number triangle: store c = arctan(5/7) and sin(c) + cos(c) shows about 1.3950.

Your turn

Problem 1. sin(a°) = 0.5 and cos(b°) = 0.99, where 0 < a < 90 and 0 < b < 90. What is the value of 2cos((90 - a)°)cos(b°) + sin(a°)sin((90 - b)°)?

Problem 2. For an acute angle t, sin(t°) = 0.28. What is the value of cos²(t°)?

SAT-style questions written by TTA. Try both before you read the answers.

Answers.

1. 1.485. Store a = arcsin(0.5) and b = arccos(0.99), then type 2cos(90 - a)cos(b) + sin(a)sin(90 - b). By hand, cos(90 - a) = sin(a) and sin(90 - b) = cos(b), so the expression is 3sin(a)cos(b) = 3(0.5)(0.99) = 1.485.
2. 0.9216. Store t = arcsin(0.28), then type cos(t)^2. By hand, cos² = 1 - sin² = 1 - 0.0784 = 0.9216.

Is the expression a constant? Test two pairs

Some questions show a long expression in two angles and ask for its value. If the question expects one number, the expression must be a constant, and two test pairs will show it.

Take (sin(a)cos(b) + cos(a)sin(b))² + (cos(a)cos(b) - sin(a)sin(b))². Store a = 37 and b = 52 on two lines, then type the expression on a third:

(sin(a)cos(b) + cos(a)sin(b))^2 + (cos(a)cos(b) - sin(a)sin(b))^2

Desmos shows 1. Change the values to a = 13 and b = 71, and it still shows 1. The answer is 1. The algebra behind it: the first bracket is sin(a + b), the second is cos(a + b), and sin² + cos² = 1. Desmos gets you to 1 without the angle-sum formulas.

When algebra is faster

College Board's calculator policy says some Math questions are better done without a calculator, even though you are allowed one. If a choice reads sin(x°) and the question asks about cos((90 - x)°), the identity answers it faster than typing six lines. Reach for Desmos when the angle comes as a decimal, or when two choices look close and you want proof.

Mistakes to avoid

• Radian mode on a degree question. sin(30) returns about -0.988 in radians instead of 0.5, and that wrong value carries into each line that uses it.
• Test values stored in x, y or θ. x = 37 draws a line, and θ = arctan(3/4) returns an error. Use a, b or t.
• Trusting one test value. At a = 45, sin(a) and cos(a) both show 0.7071, so a cofunction question can look like it has two right answers. Change the value once before you choose.

Practice next

• Work through the free Right-Triangle Trigonometry lesson notes.
• Set up sin, cos and tan from a triangle with SAT trig ratios on Desmos.
• Check radian answers with the unit circle on Desmos.
• Mix trig in with other topics in the TTA SAT question bank.

Checked against College Board's calculator policy and Desmos's College Board testing calculator on September 26, 2026. Every value on this page was recomputed and entered in that calculator in degree mode. The Test Advantage is independent of College Board and Desmos.