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Topic 1: Basic Trigonometric Identities (Quotient, Reciprocal, Pythagorean, Cofunction, and Even-Odd) Directions: Use reciprocal or quotient identities to find each exact value. 1.
Find a missing leg or hypotenuse of a right triangle using the Pythagorean Theorem. Both basic and complex problems that require more than one step included. Use the Pythagorean Theorem Converse to determine if a triangle is acute, right, or obtuse. Solve word problems using the Pythagorean Theorem.
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- Pythagorean Trig Identities
- Proof of Pythagorean Identity sin²θ + Cos²θ = 1
- Proof of Pythagorean Identity Sec²θ - Tan²θ = 1
- Proof of Pythagorean Identity Csc²θ - Cot²θ = 1
All Pythagorean trig identities are mentioned below together. Each of them can be written in different forms by algebraic operations. i.e., each Pythagorean identity can be written in 3 forms as follows: 1. sin2θ + cos2θ = 1 ⇒ 1 - sin2θ = cos2 θ ⇒ 1 - cos2θ = sin2θ 2. sec2θ - tan2θ = 1 ⇒ sec2θ = 1 + tan2θ ⇒ sec2θ - 1 = tan2θ 3. csc2θ - cot2θ = 1 ⇒ ...
Applying the Pythagoras theorem to the triangle, we get a2 + b2 = c2 Dividing each term on both sides by c2, a2 / c2 + b2 / c2 = c2 / c2 (a / c)2 + (b / c)2= 1 (cos θ)2 + (sin θ)2= 1 (or) sin2θ + cos2θ = 1 Hence proved.
Again, by Pythagoras theorem a2 + b2 = c2 Dividing each term on both sides by a2, a2 / a2 + b2 / a2 = c2 / a2 1 + (b / a)2 = (c / a)2 1 + (tan θ)2 = (sec θ)2 (or) sec2θ - tan2θ = 1 Hence proved.
By Pythagoras theorem, a2 + b2 = c2 Dividing each term on both sides by b2, a2 / b2 + b2 / b2 = c2 / b2 (a / b)2 + 1 = (c / b)2 (cot θ)2 + 1 = (csc θ)2 (or) csc2θ - cot2θ = 1 Hence proved. 1. Pythagorean identities are used to prove other trigonometric identies. Example: Prove the identity sin4x - cos4x = sin2x - cos2x. Solution: We can write LHS =...
In this Gina Wilson All Things Algebra 2014 The Pythagorean Theorem review, we will delve into the intricacies of the platform, exploring its features, content diversity, user interface, and the overall reading experience it promises.
• Pythagorean Theorem • Special Right Triangles • Trigonometric Functions (sin, cos, tan, csc, sec, cot) • Finding Side and Angle Measures • Applications: Angle of Elevation and Depression • Angles in Standard Position • Converting between Degrees and Radians • Coterminal and Reference Angles
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This Right Triangles and Trigonometry Unit Bundle contains guided notes, homework assignments, three quizzes, a study guide and a unit test that cover the following topics:• Pythagorean Theorem and Applications• Pythagorean Theorem Converse and Classifying Triangles • Special Right Triangles: 45-45-90 and 30-60-90• Similar Right ...
• Use the Pythagorean Theorem to solve problems in right triangles, including real -world situations. • Use the Pythagorean Theorem Converse to prove whether a right triangle can be formed given three side lengths. • Solve for missing side lengths in 45 -45-90 and 30-60-90 triangles.
