IllinoisTrigonometry
Illinois High School Trigonometry Curriculum
Video lessons and practice for every Trigonometry topic. Aligned to Illinois Learning Standards for Math so students can keep up with class or get ahead.
Illinois High School Trigonometry Curriculum | StudyPugHelp
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.C.8 | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. |
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. |
Illinois High School Trigonometry Overview
Trigonometry is a foundational course in the Illinois high school math sequence. It bridges the gap between algebra and pre-calculus, introducing students to angle measurement, the unit circle, and the six trigonometric functions. Mastery of these concepts is essential for success in calculus and standardized tests like the ACT and SAT.
Key Topics in This Course
- Radian Measure and the Unit Circle: Students learn to measure angles in radians, connect arc length to radius, and use the unit circle to evaluate sine, cosine, and tangent for any real number.
- Trigonometric Functions: The course extends trig functions to all real numbers and explores symmetry, periodicity, amplitude, frequency, and midline for modeling real-world phenomena.
- Inverse Trigonometric Functions: By restricting domains, students construct inverse functions and use them to solve equations that arise in applied contexts.
- Trigonometric Identities: Students prove the Pythagorean identity and the addition and subtraction formulas for sine, cosine, and tangent, then apply them to solve problems.
- Right Triangle Trigonometry: Using similarity, students define trig ratios for acute angles, apply complementary angle relationships, and solve applied problems with the Pythagorean Theorem.
- Laws of Sines and Cosines: Students derive and prove both laws, derive the triangle area formula A = ½ab sin(C), and apply these tools to right and non-right triangles.
- Arc Length and Sector Area: Students derive the proportional relationship between arc length and radius and use it to find the area of a sector.
How This Aligns to Illinois Learning Standards for Math
Every topic in this course is mapped to the Illinois Learning Standards for Math. StudyPug lessons follow the same sequence Illinois schools use, so students always know they are studying the right material for their class and upcoming assessments.
How StudyPug Helps Illinois Trigonometry Students
StudyPug provides short video lessons, worked examples, and practice problems for every chapter listed above. Students can search by topic, watch a lesson before a test, or review a concept they missed in class. Parents can track progress and make sure their student stays on pace with the Illinois curriculum.