MinnesotaTrigonometry
Minnesota High School Trigonometry Curriculum
Video lessons and practice for every trigonometry topic. Aligned to Minnesota Academic Standards Math. Get help with radian measure, the unit circle, trig identities, and more.
Minnesota 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. |
High School Trigonometry in Minnesota
Minnesota high school trigonometry is built around the Minnesota Academic Standards Math. Students move from foundational geometry into the language of radian measure, the unit circle, and trigonometric functions. Mastery of these concepts is essential for success in pre-calculus, calculus, and standardized assessments including the MCA.
Key Topics Covered
- Radian Measure and the Unit Circle: Understand radian measure as arc length on the unit circle and extend trig functions to all real numbers.
- Special Triangles and Exact Values: Use 30-60-90 and 45-45-90 triangles to find exact values of sine, cosine, and tangent for π/6, π/4, and π/3.
- Symmetry and Periodicity: Explore odd and even properties of trig functions and model periodic phenomena with specified amplitude, frequency, and midline.
- Inverse Trigonometric Functions: Restrict domains to construct inverses and use them to solve equations in real-world modeling contexts.
- Trigonometric Identities: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and the addition and subtraction formulas for sine, cosine, and tangent.
- Right Triangle Trigonometry: Apply trig ratios and the Pythagorean Theorem to solve applied problems involving right triangles.
- Laws of Sines and Cosines: Prove and apply both laws to find unknown measurements in right and non-right triangles.
- Arc Length and Sector Area: Derive arc length proportionality and the formula for the area of a sector using radian measure.
How StudyPug Helps Minnesota Trigonometry Students
StudyPug provides video lessons and practice problems for every trigonometry standard in the Minnesota Academic Standards Math. Students can search by topic, watch a focused lesson, and immediately practice with similar problems. Whether catching up after a missed class or pushing ahead before an exam, StudyPug fits into any study schedule.
All content is accessible on computers, tablets, and phones — so Minnesota students can get help at home, in the library, or anywhere else they study.