HawaiiHawaii High School Trigonometry Curriculum
Video lessons and practice for every high school trigonometry topic. Aligned to Hawaii Common Core Standards Math for high school students.
Hawaii 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. |
Hawaii High School Trigonometry: Topics and Standards
Hawaii high school trigonometry covers a wide range of concepts aligned to Hawaii Common Core Standards Math. Students explore radian measure, the unit circle, trigonometric functions, inverse functions, identities, and triangle laws. These topics are essential preparation for precalculus, calculus, and the SBAC Grade 11 assessment.
Radian Measure and the Unit Circle
Students begin by understanding radian measure as the arc length on the unit circle subtended by an angle. The unit circle then extends trigonometric functions to all real numbers, interpreted as radian measures. Using special triangles, students find exact values of sine, cosine, and tangent for common angles such as π/6, π/4, and π/3. StudyPug's video lessons walk through each of these ideas step by step.
Trigonometric Functions and Their Properties
This section covers symmetry and periodicity of trig functions using the unit circle, modeling periodic phenomena with specified amplitude, frequency, and midline, and understanding how restricting domains allows inverse functions to be constructed. Students also learn to solve equations using inverse trig functions in real-world modeling contexts.
Trigonometric Identities
- Prove and apply the Pythagorean identity: sin²(θ) + cos²(θ) = 1
- Prove and use addition and subtraction formulas for sine, cosine, and tangent
- Find unknown trig values given one ratio and the quadrant of the angle
Right Triangle Trigonometry and Geometry Foundations
Students revisit precise definitions of geometric figures and develop definitions of transformations. They then connect similarity to trigonometric ratios for acute angles, use the relationship between sine and cosine of complementary angles, and apply trig ratios with the Pythagorean Theorem to solve applied problems.
Laws of Sines and Cosines
Advanced triangle work includes deriving the area formula A = ½ab sin(C), proving the Laws of Sines and Cosines, and applying them to find unknown measurements in both right and non-right triangles. Arc length and sector area formulas are also derived using similarity and radian measure.
How StudyPug Supports Hawaii Trigonometry Students
Every topic on this page is covered by a video lesson and matching practice problems aligned to Hawaii Common Core Standards Math. Students can search for any standard, watch the explanation, and practice until they feel confident. Parents can track progress, and students can use StudyPug on any device.