Will this help with my child's high school trigonometry homework?

Yes. StudyPug covers every Illinois Learning Standards Trigonometry topic, including the unit circle, inverse trig functions, and the Law of Cosines, so your child can find help for exactly what their teacher assigned.

How long are the video lessons?

Most video lessons run between five and fifteen minutes. They focus on one concept at a time, so your child can watch just the lesson they need without sitting through an entire class period.

Is there a state test for high school trigonometry in Illinois?

Illinois does not administer a dedicated statewide trigonometry test. High school math assessments in Illinois typically focus on algebra and related courses; check with your child's school for any course-level or district assessments.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, and computers, so your child can practice the unit circle or work through Law of Sines problems wherever they study, with no app download required.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can see the content before committing. Every paid plan also comes with a 30-day money-back guarantee if it is not the right fit.

IL High School Trigonometry Curriculum

Give your high schooler the support they need to work through Illinois trigonometry with confidence. Every strand from the unit circle to the Laws of Sines and Cosines is covered.

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IL High School Trigonometry Curriculum

IDStandardStudyPug Topic

CC.HSF.TF.A.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
- Converting between degrees and radians
- Trigonometric ratios of angles in radians
- Radian measure and arc length
CC.HSF.TF.A.2Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
- Unit circle
CC.HSF.TF.A.3Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.
- Find the exact value of trigonometric ratios
- Solving expressions using 45-45-90 special right triangles
- Solving expressions using 30-60-90 special right triangles
CC.HSF.TF.B.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
- Graphing transformations of trigonometric functions
- Determining trigonometric functions given their graphs
CC.HSF.TF.B.6Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
- Solving two-step linear equations using addition and subtraction: ax + b = c
CC.HSF.TF.B.7Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
- Evaluating inverse trigonometric functions
CC.HSF.TF.C.8Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
- Pythagorean identities
CC.HSF.TF.C.9Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
- Sum and difference identities
- Double-angle identities
- Cofunction identities
CC.HSG.CO.A.1Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
- Parallel and perpendicular line segments
- Line symmetry
- Angles in a circle
- Chord properties
- Circles and circumference
CC.HSG.SRT.C.6Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- Use sine ratio to calculate angles and sides (Sin = o / h)
- Use tangent ratio to calculate angles and sides (Tan = o / a)
CC.HSG.SRT.C.7Explain and use the relationship between the sine and cosine of complementary angles.
- Use cosine ratio to calculate angles and sides (Cos = a / h)
- Cofunction identities
CC.HSG.SRT.C.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
- Combination of SohCahToa questions
- Word problems relating ladder in trigonometry
- Word problems relating guy wire in trigonometry
- Other word problems relating angles in trigonometry
CC.HSG.SRT.D.9Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
- Area of triangles: 1/2 a*b sin(C)
CC.HSG.SRT.D.10Prove the Laws of Sines and Cosines and use them to solve problems.
- Law of sines
- Law of cosines
CC.HSG.SRT.D.11Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
- Applications of the sine law and cosine law
CC.HSG.C.B.5Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
- Radian measure and arc length
- Converting between degrees and radians
- Trigonometric ratios of angles in radians

Trigonometry

About High School Illinois Trigonometry

Illinois follows the Illinois Learning Standards for high school math, organized around conceptual understanding, procedural fluency, and application. In Trigonometry, students explore radian measure and the unit circle, trigonometric functions and their inverses, the Pythagorean identity, addition and subtraction formulas, right triangle ratios, and the Laws of Sines and Cosines. StudyPug provides video lessons and practice problems aligned to every strand so students can get unstuck and move forward at their own pace.

Strands: unit circle and radian measure, trigonometric functions and inverses, Pythagorean and addition/subtraction identities, right triangle ratios, and Laws of Sines and Cosines
Video lessons covering every Illinois Learning Standards Trigonometry topic
Practice problems and step-by-step solutions for each concept
Content aligned to the Illinois Learning Standards for high school math

Curriculum topics by strand

Browse lessons and practice problems organized by strand and aligned to the Illinois Learning Standards for high school Trigonometry.

Topic includes:

Practice

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Standard

StudyPug Topic

Illinois High School Trigonometry Topics

Unit circle and radian measure: students learn radian measure as arc length on the unit circle and use it to extend trigonometric functions to all real numbers.
Trigonometric functions, symmetry, and periodicity: the unit circle is used to explore odd and even symmetry, periodicity, and modeling periodic phenomena with specified amplitude, frequency, and midline.
Inverse trigonometric functions: students restrict domains to construct inverses and use them to solve trigonometric equations that arise in real-world modeling contexts.
Pythagorean identity and addition/subtraction formulas: students prove sin^2(x) + cos^2(x) = 1 and the addition and subtraction formulas for sine, cosine, and tangent, then apply them to solve problems.
Right triangle trigonometry: work covers the definitions of trigonometric ratios for acute angles, the relationship between sine and cosine of complementary angles, and applying ratios with the Pythagorean Theorem to solve applied problems.
Laws of Sines and Cosines: students derive and prove both laws and use them to find unknown measurements in right and non-right triangles, including deriving the triangle area formula A = 1/2 ab sin(C) and the formula for the area of a sector.

How StudyPug Helps Illinois High School Trigonometry Students

When a student gets stuck on a concept like inverse trig functions or the Law of Cosines, they can go straight to the relevant video lesson, watch a step-by-step explanation, and then work through practice problems to build confidence before returning to their homework.

Because StudyPug organizes content by strand and aligns it to the Illinois Learning Standards, students spend less time searching and more time actually learning the trigonometry their class requires.

Aligned to Illinois High School Trigonometry Curriculum

Every lesson and practice problem on StudyPug is built around the Illinois Learning Standards for high school math, so the content your child sees matches what their teacher is covering in class - from radian measure and the unit circle through the Laws of Sines and Cosines.

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Written by the StudyPug Math Team

Last updated June 5, 2026

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