Curated OER
Pythagorean Identities
In this Pythagorean identities activity, 11th graders solve 10 different problems that include applying various Pythagorean identities in each. First, they determine the values of tangent, secant, cosecant, and cosine given the other...
Shodor Education Foundation
Pythagorean Theorem
Most adults remember learning about the Pythagorean theorem, but they don't all remember how to use it. The emphasis here is on developing an intuitive understanding of how and when to use the theorem. Young mathematicians explore...
EngageNY
Trigonometry and the Pythagorean Theorem
Ancient Egyptians sure knew their trigonometry! Pupils learn how the pyramid architects applied right triangle trigonometry. When comparing the Pythagorean theorem to the trigonometric ratios, they learn an important connection that...
Willow Tree
The Pythagorean Theorem
There isn't a more popular geometry formula than the Pythagorean Theorem! Learners understand the special side relationships in a right triangle. They use the Pythagorean Theorem to find missing sides and to solve problems. They begin...
EngageNY
Proving Trigonometric Identities
Young mathematicians first learn the basics of proving trigonometric identities. They then practice this skill on several examples.
EngageNY
The Power of Algebra—Finding Pythagorean Triples
The Pythagorean Theorem makes an appearance yet again in this lesson on polynomial identities. Learners prove a method for finding Pythagorean triples by applying the difference of squares identity.
Curated OER
Pythagorean Theorem
For this measurement lesson, learners examine the Pythagorean Theorem, perimeter, and areas of right triangles. They record their measurements and research their findings on a grid.
Illustrative Mathematics
Trigonometric Ratios and the Pythagorean Theorem
Take an alternative route with trigonometry and let learners connect a tweaked version of the pythagorean theorem to the original in terms of triangle sides. The assignment leads participants towards deriving the Pythagorean identity...
CK-12 Foundation
Pythagorean Theorem for Solving Right Triangles: Solving the Triangle
Observe the change in the trigonometric ratios as angles vary. An interactive provides the values of trigonometric ratios for both acute angles in a right triangle. Pupils create a right triangle to match given criteria and find the...
Curated OER
6.5 Skill Builder: Trigonometric Identities
In this trigonometric identities worksheet, students solve 16 multi-part short answer problems. Students use the quotient identity and Pythagorean identity to simplify trigonometric expressions. Students factor trigonometric expressions.
Curated OER
Proof of Identity
Students explore trigonometric identities. In this Algebra II lesson, students use graphing to verify the reciprocal identities. Using Cabri Jr, students investigate the Pythagorean trigonometric identities and the geometric c proofs...
EngageNY
What Is a Trigonometric Identity?
Protect yourself from identity theft! Establishing a strong understanding of the Pythagorean identity allows learners to prove that sine^2x + cos^2x = 1. They then use the identity to find sine or cosine ratios given the other.
Inside Mathematics
Hopewell Geometry
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
Alabama Learning Exchange
"I Saw the Sine"
Discover trigonometric ratios that complement each other. Using two videos, the lesson introduces the trigonometric ratios. The class discovers the relationship between the sine and cosine of complementary angles.
Curated OER
Trigonometric Expressions and Identities
For this college level Pre-calculus worksheet, students use the trigonometric identities to factor and simplify trigonometric expressions. Students use algebra to prove various trigonometric identities. The three page worksheet...
Curated OER
Pythagorean Theorem
Students solve problems using the Pythagorean Theorem. In this geometry lesson, students identify the sides and angles of a right triangle. They find the different trigonometric ratios and solve using sine, cosine and tangent.
Flipped Math
Reference Triangles
It is all about where the side is located. Pupils use their knowledge of angles in standard position to find reference angles. They use the Pythagorean Theorem to find lengths along a terminal side of an angle to determine the exact...
CK-12 Foundation
Basic Trigonometric Functions: Ladder Length
Climb the ladder to trigonometry. The interactive introduces trigonometric ratios and finding lengths of sides of right triangles created by a ladder and a building. Learners use the interactive to create triangles by moving the top of...
Curated OER
Trigonometric Ratios
In this trigonometric ratios worksheet, 10th graders solve 9 different problems that include determining the trigonometric ratios of each triangle. First, they determine the sides and angles of a right triangle that is shown in each...
Curated OER
Identities and Trigonometric Values
Young scholars solve trigonometric equations. In this precalculus instructional activity, students prove trigonometric identities using the Pythagorean Theorem. They apply the addition formulas for sine and cosine to prove different...
Curated OER
Right Triangles and The Pythagorean Theorem
Students play a game to reinforce concepts of the Pythagorean Theorem. In this geometry lesson, students find the missing angle and lengths of a right triangle. They use properties of trigonometry about sine, cosine and tangent to solve...
Curated OER
Further Trigonometry
For this trigonometry worksheet, students solve and complete 5 various types of problems. First, they find the exact ratios for each trigonometric function. Then, students use the expansion to find the exact value of a given trig...
Mathematics Vision Project
Similarity and Right Triangle Trigonometry
Starting with similar triangles and dilation factors, this unit quickly and thoroughly progresses into the world of right triangle features and trigonometric relationships. Presented in easy-to-attack modules with copious application...
Curated OER
Powers of Trig Functions
In this trigonometric worksheet, students solve integrals by substitution and the Pythagorean theorem. Students use their trigonometric functions to solve problems. This four-page worksheet contains 20 problems.