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May 8, 2013 · Lecture Notes Trigonometric Identities 1 page 4 6. cos2 x = cscxcosx tanx+cotx Solution: We will start with the right-hand side. We will re-write everything in terms of sinx and cosx and simplify. We will again run into the Pythagorean identity, sin2 x+cos2 x = 1. RHS = cscxcosx tanx+cotx = 1 sinx cosx sinx cosx + cosx sinx = 1 sinx cosx 1 sin2 ...
Identities worksheet 3.4 name: 2. 1 + cos x = esc x + cot x sinx 4. ... Trig Identity Quiz Prove the following identity 1) 2 cos etan ecsc e= 2 2) ...
Example: Given. 3 =. 4. a) Use the Pythagorean Theorem. c) Given. 1 = −. 4. b) Use the Pythagorean Identity. 3 Types of Problems: Simplifying (write in simplest terms) Verifying (show why the identity is true by working from one side to the other) Evaluating (use trig identities to solve)
Example 1: Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant. a. tan𝜃cos𝜃 b. 1−cos 2𝜃 cos2𝜃 c. cos𝜃csc𝜃 d. sin𝜃sec𝜃 tan𝜃 Example 2: Simplify the complex fraction. a. 2 3 4 15 b. 4 5 4 35 c. 2 5 3 5 d. 1 2 2 sin𝜃= 1 csc𝜃 csc𝜃= 1 sin𝜃 cos𝜃= 1 ...
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In this section, we will begin an examination of the fundamental trigonometric identities, including how we can verify them and how we can use them to simplify trigonometric expressions. Verifying the Fundamental Trigonometric Identities . Identities enable us to simplify complicated expressions.
Simplifying trigonometric expressions often takes some trial and error, but the following strategies may be helpful. o Use algebra and fundamental identities to simplify the expression. o Sometimes, writing all functions in terms of sines and cosines may help.
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