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Home Question Bank Math Trigonometry Archive 2025 January 19

Trigonometry Questions from Jan 19,2025

Browse the Trigonometry Q&A Archive for Jan 19,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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a) \( \sin \frac{4 \pi}{9} \) Find the exact value of the expression. \( \tan \left[\sin ^{-1}\left(\frac{4}{9}\right)\right] \) Select the correct choice and fill in any answer boxes in your choice below. A. \( \tan \left[\sin ^{-1}\left(\frac{4}{9}\right)\right]=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. There is no solution. Find the exact value of the expression. \( \cos ^{-1}\left(\sin \frac{4 \pi}{3}\right) \) Select the correct choice and fill in any answer boxes in your choice below. A. \( \cos ^{-1}\left(\sin \frac{4 \pi}{3}\right)=\square \) (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.) B. There is no solution. Find the exact value of the expression. \[ \sin \left[\tan ^{-1}(-\sqrt{3})\right] \] Select the correct choice and fill in any answer boxes in your choice below. A. \( \sin \left[\tan ^{-1}(-\sqrt{3})\right]= \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. There is no solution. Find the exact value of the expression. \( \sec \left[\cos ^{-1}\left(\frac{1}{2}\right)\right] \) Select the correct choice and fill in any answer boxes in your choice below. A. \( \sec \left[\cos ^{-1}\left(\frac{1}{2}\right)\right]=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. There is no solution. s; \( \theta \) y ason los \( \ddagger \) agudos y \( \sec \theta=2 \sqrt{3} \) Find the exact value of the expression. \( \cos \left[\sin ^{-1}\left(-\frac{1}{2}\right)\right] \) Select the correct choice and fill in any answer boxes in your choice below. A. \( \cos \left[\sin ^{-1}\left(-\frac{1}{2}\right)\right]=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. There is no solution. 17. Simplify \( \cos \left(\frac{3 \pi}{4}+x\right)+\sin \left(\frac{3 \pi}{4}-x\right) \) A triangle has one side of length 14 units, another side of length 9 units, and includes an angle of 45 degrees. Determine the area of the triangle using the appropriate trigonometric identity. \( \sin 4 x \sin 3 x + \cos 4 x \cos 3 \)
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