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Trigonometry

Master Trigonometry

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Unit circle was impossible until StudyPug. The video lessons made radians finally click. Went from D to B+ in 6 weeks.

Jordan Kim

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Why Trigonometry Students Choose StudyPug

The complete learning system to master trigonometry

Search with Photo

Search with Photo

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Expert Video Teaching

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Unlimited Practice

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Work through similar problems until concepts stick.

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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

Trig identities were killing my grade. The step-by-step videos showed me every detail. Aced my final and raised my GPA.

Alex Patel

Law of Sines made no sense for weeks. The AI found exactly what I needed. Got an A on my triangle unit test.

Riley Martinez

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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, practice problems, step-by-step solutions, and progress tracking for every topic including unit circle, identities, and Laws of Sines and Cosines.

How does photo search work?

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

Are the teachers certified Illinois educators?

Yes! Our teachers are certified educators who understand Illinois curriculum and create lessons specifically for trigonometry standards.

Can I use StudyPug on my phone or tablet?

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

How will StudyPug help me prepare for the SAT?

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

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