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Trigonometry

Master Trigonometry

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Unit circle was impossible until StudyPug. The video lessons made identities click. Went from D to B+ in six weeks.

Jordan Kim

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Why Trigonometry Students Choose StudyPug

The complete learning system to master Trigonometry

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Expert Video Teaching

Certified teachers break down unit circle, trig identities, and law of sines step-by-step

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Unlimited Practice

5,000+ teacher-created practice questions prepare you for Trigonometry exams

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Practice & Master

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Illinois Trigonometry Help: Master Concepts FastHelp

Print

ID

Standard

StudyPug Topic

CC.HSF.TF.A.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

CC.HSF.TF.A.2

Explain 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.

CC.HSF.TF.A.3

Use 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.

CC.HSF.TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

CC.HSF.TF.B.6

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

CC.HSF.TF.B.7

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

CC.HSF.TF.C.8

Prove 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.

CC.HSF.TF.C.9

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

CC.HSG.CO.A.1

Know 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.

CC.HSG.SRT.C.6

Understand 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.

CC.HSG.SRT.C.7

Explain and use the relationship between the sine and cosine of complementary angles.

CC.HSG.SRT.D.9

Derive 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.

CC.HSG.SRT.D.10

Prove the Laws of Sines and Cosines and use them to solve problems.

CC.HSG.SRT.D.11

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

CC.HSG.C.B.5

Derive 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.
Complete Illinois Trigonometry Coverage

Trigonometry Lessons

36

Video Explanations

221

Practice Problems

300

Illinois Standards

100% Aligned

Why Illinois Trigonometry Students Love StudyPug

SAT Math Preparation

SAT Math Preparation

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Certified Teachers

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Success Stories

Law of Cosines made no sense. The AI photo search found perfect lessons instantly. Aced my final with 92%.

Alex Rodriguez

Spent hours confused about inverse trig functions. StudyPug's videos explained everything in 20 minutes. Game changer.

Taylor Chen

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Frequently Asked Questions

Everything you need to know about mastering Trigonometry with StudyPug

What does Trigonometry coverage include?

Complete Trigonometry curriculum with video lessons on unit circle, trig identities, inverse functions, and triangle solutions. Includes practice problems, step-by-step solutions, and progress tracking for every topic.

How does the AI photo search work?

Take a photo of any trig problem, and our AI finds the exact lesson teaching that concept. It's like having a personal tutor who knows exactly what you need for your homework.

Are the teachers certified Illinois educators?

Yes! Our teachers are certified Illinois educators who understand state curriculum and create lessons specifically for Trigonometry standards taught in Illinois schools.

Can I use StudyPug on my phone or tablet?

Absolutely! StudyPug works on desktop, tablet, and mobile. Your progress syncs automatically so you can study trigonometry anywhere, anytime.

How will StudyPug help me prepare for the SAT Math?

We include SAT-style trigonometry practice questions and teach the exact concepts tested. Students report significantly improved test scores and confidence on exam day.

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