NevadaNevada High School Trigonometry Curriculum
Video lessons and practice for every Trigonometry topic. Aligned to Nevada Academic Content Standards Math. Get help with homework anytime.
Nevada 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. |
Nevada High School Trigonometry: Topics and Standards
Nevada high school Trigonometry follows the Nevada Academic Content Standards Math, which draw on the standards for trigonometric functions, geometric definitions, and similarity. StudyPug covers every topic students encounter in class, from the basics of radian measure to the advanced applications of the Laws of Sines and Cosines.
Unit Circle and Radian Measure
Students start by understanding radian measure as the length of an arc on the unit circle subtended by an angle. From there, they learn how the unit circle extends trigonometric functions to all real numbers. Special triangles — 30-60-90 and 45-45-90 — help students find exact values of sine, cosine, and tangent for key angles like π/6, π/4, and π/3.
Trigonometric Functions and Their Properties
Nevada Trigonometry students study the symmetry and periodicity of trig functions using the unit circle. They learn to model periodic phenomena by choosing functions with the right amplitude, frequency, and midline. Understanding odd and even functions deepens their grasp of how sine, cosine, and tangent behave across all real numbers.
Inverse Trigonometric Functions
By restricting trig functions to intervals where they are always increasing or always decreasing, students can construct inverse functions. These inverses are used to solve trigonometric equations that appear in real-world modeling problems. Students evaluate solutions using technology and interpret results in context.
Trigonometric Identities
A key milestone in Trigonometry is proving the Pythagorean identity: sin²(θ) + cos²(θ) = 1. Students use this identity to find unknown trig values given partial information and a quadrant. They also prove and apply the addition and subtraction formulas for sine, cosine, and tangent to solve a wide range of problems.
Right Triangle Trigonometry
- Define trigonometric ratios using side ratios in right triangles
- Explain the relationship between sine and cosine of complementary angles
- Use trigonometric ratios and the Pythagorean Theorem to solve applied problems
Laws of Sines and Cosines
Students derive the formula A = ½ab sin(C) for triangle area and prove both the Law of Sines and the Law of Cosines. These tools allow students to solve for unknown sides and angles in both right and non-right triangles, which is essential for applied geometry and pre-calculus work.
Arc Length and Sector Area
Using similarity, students derive the fact that arc length is proportional to radius. They define radian measure as the constant of proportionality and derive the formula for the area of a sector. These concepts connect algebra, geometry, and trigonometry in a unified framework.