Simplifying Trigonometric Expressions

The process of Simplifying Trigonometric Expressions is primarily about distilling complicated or long-winded trigonometric equations into more manageable forms. This is achieved by utilizing trigonometric identities, engaging in algebraic adjustments, and carrying out arithmetic operations. Simplification serves to make these expressions more digestible, user-friendly, and implementable in problem-solving, particularly within the realms of calculus and physics.

Finding the Exact Value

Give the exact value of the expression without using a calculator. cos⁡(tan−1⁡43−tan−1⁡(−815)) cos⁡(tan−1⁡43−tan−1⁡(−815))= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
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Finding the Value Using the Unit Circle

Find the value of sin⁡(330∘) using the unit circle
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Expanding Trigonometric Expressions

Perform the indicated operation and simplify the result so that there are no quotients. (5+sin⁡t)2+cos2⁡t The simplified form, with no quotients, of (5+sin⁡t)2+cos2⁡t is (Do not factor.)
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Expanding Using Double-Angle Formulas

Rewrite sin⁡(2tan−1⁡u) as an algebraic expression in u. sin⁡(2tan−1⁡u)=
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Expanding Using Triple-Angle Formulas

Simplify the expression 2sin⁡(3x)
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Expanding Using Sum/Difference Formulas

Use a sum or difference formula to find the exact value of the following. sin⁡29π42cos⁡π7+cos⁡29π42sin⁡π7
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Simplify Using Pythagorean Identities

The expression below simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify the expression. cos2⁡xsin2⁡x+csc⁡xsin⁡x cos2⁡xsin2⁡x+csc⁡xsin⁡x=
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Simplify by Converting to Sine/Cosine

MWF Armando Ramirez This quizz 5 point(s) possible This question: 1 point(s) possible Submit quiz The expression cos⁡x−sin2⁡xcos⁡x⋅csc⁡x is to be the left hand side of an equation that is an identity. Which one of the following four expressions can be used as the right hand side of the equation to complete the identity?
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Inverting Trigonometric Expressions

Write the expression as an algebraic (nontrigonometric) expression in u, for u>0. csc⁡(arccot4−u2u) csc⁡(arccot4−u2u)=
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Finding the Trig Value of an Angle

Write the expression as a single function of α. cos⁡(0∘+α) Choose the correct answer below. A. −cos⁡α B. cos⁡α C. −sin⁡α D. sin⁡α
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Expanding Using De Moivre's Theorem

Expand the expression (1+i3)6 using De Moivre's theorem.
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