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Pre-Calculus: Trigonomentry

Indiana Pre-Calculus: Trigonometry Curriculum

Video lessons and practice for every Pre-Calculus Trigonometry topic. Aligned to Indiana Academic Standards for Math. Master radian measure, the unit circle, trig identities, and more.

Indiana Pre-Calculus Trigonometry Curriculum | StudyPugHelp

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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.

Indiana Pre-Calculus Trigonometry: What Students Learn

Indiana Pre-Calculus Trigonometry is one of the most concept-rich courses in high school math. Students move from the basics of angle measurement all the way through advanced identities and the Laws of Sines and Cosines. StudyPug covers every topic with video lessons and practice problems aligned to Indiana Academic Standards for Math.

Radian Measure and the Unit Circle

Students begin by understanding radian measure — defining an angle's measure as the length of the arc on the unit circle it subtends. From there, the unit circle becomes the foundation for extending trigonometric functions to all real numbers. StudyPug video lessons walk through how to read the unit circle, identify coordinates, and use special triangles for angles like π/3, π/4, and π/6.

Trigonometric Functions and Their Properties

This course explores sine, cosine, and tangent in depth — including symmetry, periodicity, and how to use these functions to model real-world periodic phenomena. Students also learn about amplitude, frequency, and midline when fitting trig functions to data.

  • Odd and even symmetry of trig functions using the unit circle
  • Periodic behavior and graphing trig functions
  • Choosing the right trig function for a modeling problem

Inverse Trigonometric Functions

Understanding why trig functions must be restricted to specific domains before their inverses can be defined is a key concept in this course. Students learn to use inverse functions to solve equations that come up in applied and modeling contexts.

Trigonometric Identities

Students prove and apply the Pythagorean identity sin²(θ) + cos²(θ) = 1, and use it to find missing trig values given one ratio and a quadrant. They also prove and use the addition and subtraction formulas for sine, cosine, and tangent to solve a range of problems.

Right Triangle Trigonometry and Geometry Foundations

Building on geometry, students revisit precise definitions of angles, circles, and line segments. They connect similarity in right triangles to the definitions of trig ratios for acute angles, and use those ratios together with the Pythagorean Theorem to solve applied problems.

  • Sine and cosine of complementary angles
  • Trig ratios for right triangle problem solving
  • Area of a triangle using A = ½ab sin(C)

Laws of Sines and Cosines

Students prove both the Law of Sines and the Law of Cosines and apply them to find unknown side lengths and angles in both right and non-right triangles. These tools are essential for applied problems in Indiana Pre-Calculus and beyond.

Arc Length and Sector Area

The course concludes with deriving the arc length formula using similarity — showing that arc length is proportional to the radius — and establishing the radian as the constant of proportionality. Students also derive the formula for the area of a sector.

StudyPug covers all of these Indiana Pre-Calculus Trigonometry topics with clear video lessons, step-by-step worked examples, and practice problems so students can build confidence at their own pace.