Identities and Trigonometric Values

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...

Young mathematicians first learn the basics of proving trigonometric identities. They then practice this skill on several examples.

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. 

In this trigonometric identities instructional activity, students solve 16 multi-part short answer problems. Students use the quotient identity and Pythagorean identity to simplify trigonometric expressions. Students factor trigonometric...

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.

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...

Students prove the theorem of Pythagoras. In this Pythagorean Theorem lesson plan, students define the different parts of a right triangle. They use the Pythagorean Theorem to solve for the missing sides and angles of a right triangle.

Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...

Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...

Discover trigonometric ratios that complement each other. Using two videos, the instructional activity introduces the trigonometric ratios. The class discovers the relationship between the sine and cosine of complementary angles.