Will this help with my child's High School trigonometry homework?

Yes. StudyPug covers every strand in the Hawaii high school trigonometry course, including the unit circle, inverse functions, and the Laws of Sines and Cosines, so students can find help the moment they get stuck on a problem.

How long are the video lessons?

Most video lessons run between five and fifteen minutes, focusing on one concept at a time. Students can pause, rewind, and rewatch as many times as they need until the idea clicks, then move straight into practice problems.

Is there a Hawaii state test for High School trigonometry?

Hawaii uses the Smarter Balanced Assessment (SBAC) for grades 3 through 8. High school end-of-course assessments vary by school and district, so check with your child's teacher for the specific exams that apply to their trigonometry course.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, laptops, and desktop computers. Students can switch between devices without losing their place, making it easy to study at home, in the library, or anywhere else.

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, so there is no risk in giving it a try.

HI High School Trigonometry Curriculum

Give your high schooler the support they need to succeed in trigonometry. Our lessons and practice problems follow what Hawaii schools teach, from the unit circle to the Laws of Sines and Cosines.

HI 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 Hawaii Trigonometry

Hawaii follows the Hawaii Content Standards for Mathematics, structured around conceptual understanding, procedural fluency, and real-world application. This course covers radian measure and the unit circle, trigonometric functions and their inverses, the Pythagorean identity, addition and subtraction formulas, right triangle trigonometry, and the Laws of Sines and Cosines. StudyPug provides video lessons and practice problems that match each of these strands so students can get unstuck any night of the week.

Strands: unit circle and radian measure, trigonometric functions and inverses, Pythagorean and addition/subtraction identities, right triangle trigonometry, Laws of Sines and Cosines, and arc length and sector area
Video lessons taught step by step for every topic in the course
Practice problems and worked examples aligned to Hawaii Content Standards for Mathematics
Unlimited access on any device so students can study at home or on the go

Curriculum topics by strand

Find lessons and practice for every strand, aligned to the Hawaii Content Standards for Mathematics.

Topic includes:

Practice

Video

Quiz

Standard

StudyPug Topic

HI High School Trigonometry Topics

Unit circle and radian measure: Understanding radian measure as arc length on the unit circle, extending trigonometric functions to all real numbers, and using the unit circle to explain symmetry and periodicity.
Trigonometric functions and inverses: Using special triangles to find exact values, choosing functions to model periodic phenomena, restricting domains to construct inverse functions, and solving trigonometric equations in modeling contexts.
Pythagorean and addition/subtraction identities: Proving the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 and using it to find missing values, and proving the addition and subtraction formulas for sine, cosine, and tangent.
Right triangle trigonometry: Defining trigonometric ratios for acute angles through similarity, using the sine-cosine complementary angle relationship, and applying trigonometric ratios with the Pythagorean Theorem to solve applied problems.
Laws of Sines and Cosines: Deriving the triangle area formula A = 1/2 ab sin(C), proving the Laws of Sines and Cosines, and applying them to find unknown measurements in right and non-right triangles.
Arc length and sector area: Deriving the proportionality of arc length to radius, defining radian measure as the constant of proportionality, and deriving the formula for the area of a sector.

How StudyPug Helps HI High School Trigonometry Students

When a student gets stuck on a concept like inverse trigonometric functions or the Law of Cosines, they can search for that exact topic, watch a focused video lesson, and then work through practice problems with step-by-step explanations. This means homework does not have to wait until the next school day.

StudyPug organizes content strand by strand so students can move through the Hawaii Content Standards for Mathematics in the same order their class does, or jump directly to the concept causing trouble without wading through unrelated material.

Aligned to HI High School Trigonometry Curriculum

Every lesson and practice problem on StudyPug is built around the Hawaii Content Standards for Mathematics, so the methods, vocabulary, and sequencing match what Hawaii high school trigonometry teachers expect. Students practice the same skills their class covers, from radian measure and the unit circle all the way 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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