ALEKS placement math guide
ALEKS trigonometry practice: worked examples and steps
Trigonometry is part of the precalculus end of ALEKS placement. Searching for ALEKS trig answers will not help much, because you cannot know which version of a problem you will get. The method works on any numbers. Here is each trig topic with one solved example and a link to practice with fresh problems.
Why look for the method, not the answer
A posted answer only helps if you get that exact problem. Learning the steps works on any numbers. ALEKS is also open-response, so you have to type a result you worked out yourself.
Without a calculator, trigonometry is mostly exact values: a few triangles and the unit circle. Learn those and most questions become reading and substitution.
Lemma is independent practice and is not affiliated with ALEKS or McGraw Hill. These examples are written for Lemma.
Right triangles and angle measure
In a right triangle, sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. Label the sides from the angle you are using before you write a ratio. Radians measure angles by arc length: 180 degrees is π radians, so to convert degrees to radians, multiply by π/180.
Right-triangle trigonometry
A ramp rises 3 ft over a 12 ft horizontal run. Find its angle.
- tanθ=123Opposite over adjacent, since neither side is the hypotenuse.
- θ=arctan(0.25)≈14∘Apply the inverse tangent.
Degrees and radians
Convert 135° to radians.
- 135⋅180πDegrees to radians multiplies by π/180.
- 43π135/180 reduces to 3/4.
The unit circle and trig equations
The unit circle gives the sine and cosine of the common angles. Solving a trig equation means finding every angle in the allowed range that gives the value, so check for a second answer.
Unit-circle values
Find cos(5π/6).
- reference=6π5π/6 is π/6 short of π.
- cos6π=2√3That is the 30-60-90 value.
- −2√35π/6 sits in quadrant II, where cosine is negative.
Solve trigonometric equations
Solve 2sin θ - 1 = 0 on [0, 2π).
- sinθ=21Isolate the function.
- θ=6πThat is the reference angle where sine is 1/2.
- θ=6π,65πSine is positive in quadrants I and II.
Triangles that are not right triangles
The law of sines relates each side to the sine of the angle across from it. The law of cosines extends the Pythagorean theorem to any triangle. Use the law of sines when you know a side and its opposite angle, and the law of cosines when you know two sides and the angle between them, or all three sides.
Laws of sines and cosines
Find c when a = 7, b = 9, and C = 40°.
- c2=49+81−2(7)(9)cos40∘Two sides and the included angle means the law of cosines.
- c≈5.8Evaluate and take the square root.
Graphs, identities and formulas
For a graph like y = A sin(Bx + C), A sets the height of the wave, B sets how fast it repeats, and C shifts it sideways. Identities let you replace one expression with an equal one, so each line you write should be something you can justify.
Amplitude, period, and phase
Find the amplitude, period, and shift of y = 3sin(2x - π).
- y=3sin(2(x−2π))Factor the 2 out before reading the shift.
- A=3,period=π,shift=2πrightRead each parameter off the factored form.
Trigonometric identities
Simplify (1 - cos²θ)/sin θ.
- sinθsin2θ1 - cos²θ = sin²θ.
- sinθ,sinθ=0Cancel one factor of sin θ, keeping sin θ ≠ 0 from the original denominator.
A study order
- Right-triangle ratios (sine, cosine, tangent) and the Pythagorean theorem.
- Degrees and radians, then the unit circle values.
- Simple trig equations, then graphs (amplitude, period, shift).
- Identities and the laws of sines and cosines last.
Practice these topics
Practice it on Lemma
Type each step and Lemma checks it. Free, no account, no email.
Questions
Is trigonometry on the ALEKS placement test?
It can be, depending on your course path. ALEKS adapts to your answers, so you may see it only if you place high enough. Lemma's ALEKS practice includes trigonometry topics for that top tier.
Do I need to memorize the unit circle?
Without a calculator you need the common angles, so it helps. Lemma's unit-circle topic practices those values.
Where can I find ALEKS trigonometry answers?
An answer to one problem does not carry over to a different one. The worked steps on this page and the topic pages work for any numbers.
More guides
- Example questionsWorked examples from equations, lines, factoring, rational equations, logs and sequences.
- How to passStudy order, guessing, the learning module and checking your own steps.
Sources
- University of Rhode Island: Understanding ALEKS scores FAQ: score meaning, 24-hour wait, five attempts, five hours of learning module, highest score counts, score-to-course map.
- McGraw Hill ALEKS support: PPL placement test retakes: schools set their own retake rules.
Facts checked 2026-10-14. Independent practice, not affiliated with ATI or McGraw Hill.