5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

Open Question
Evaluate each expression without using a calculator.
sin (sin⁻¹ 1/2 + tan⁻¹ (-3))
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Open Question
Solve each equation for x, where x is restricted to the given interval.
y = 3 tan 2x , for x in [―π/4, π/4]
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Open Question
Find the exact value of each real number y. Do not use a calculator.
y = cos⁻¹ (―√2/2)
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Open Question
Use a calculator to find each value. Give answers as real numbers.
cos (tan⁻¹ 0.5)
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Open Question
Use a calculator to find each value. Give answers as real numbers.
tan (arcsin 0.12251014)
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Open Question
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sin (arccos u)
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Open Question
Write each trigonometric expression as an algebraic expression in u, for u > 0.
cos (arcsin u)
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Open Question
Write each trigonometric expression as an algebraic expression in u, for u > 0.
sin (2 sec⁻¹ u/2)
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Open Question
In Exercises 1–26, find the exact value of each expression._cos⁻¹ √3/2
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Open Question
In Exercises 1–26, find the exact value of each expression._cos⁻¹ (- √2/2)
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Open Question
In Exercises 1–26, find the exact value of each expression._tan⁻¹ √3/3
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Open Question
In Exercises 1–26, find the exact value of each expression._tan⁻¹ (−√3)
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Open Question
In Exercises 1–26, find the exact value of each expression._cot⁻¹ √3
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Open Question
In Exercises 1–26, find the exact value of each expression._cot⁻¹ (−√3)
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Open Question
In Exercises 1–26, find the exact value of each expression._csc⁻¹ (− 2√3/3)
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