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Home Question Bank Math Trigonometry Archive 2025 January 21

Trigonometry Questions from Jan 21,2025

Browse the Trigonometry Q&A Archive for Jan 21,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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How many periods of the function \( y=\sin x \) are there between \( -8 \pi \leq x \leq 4 \pi \) ? \( [?] \) Suppose \( y=\sin x \) What is the \( x \)-value between 0 and \( 2 \pi \) that corresponds to a \( y \)-value of 1 ? \[ \frac{\pi}{[?]} \] What is the period of the following function? \( y=\sin x \) \( [?] \pi \) Determine the gradients of the lines with the following leaving your answers in the simplest surd form: \( \begin{array}{llll}\text { a) } 45^{\circ} & \text { b) } 30^{\circ} & \text { c) } 150^{\circ} & \text { d) } 0^{\circ}\end{array} \) \( 3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right) \) A. \( \frac{3(1+\sqrt{3} i)}{2} \) \( \begin{array}{ll}\text { C. } 3(\sqrt{3}+i) \\ \text { C. } 3(1+\sqrt{3} i) & \text { D. } \frac{3(\sqrt{3}+i)}{2}\end{array} \) What is \( \cot \left(-\frac{13 \pi}{6}\right) \) ? \( -\sqrt{[?]} \) Which angle is coterminal with \( -\frac{5 \pi}{6} ? \) \( -\frac{17 \pi}{6} \quad \frac{13 \pi}{6} \) Which angle is coterminal with \( -145^{\circ} \) ? \( -405^{\circ} \quad 625^{\circ} \quad 215^{\circ} \) A 50 foot rope on a dock is connected to a boat at a \( 35^{\circ} \) angle with the boat. How far away is the boat from the dock? \[ \text { [?] feet } \] Round your answer to the nearest hundredth. Perform the following operations on these complex numbers. \( 10\left(\cos 45^{\circ}+i \sin 45^{\circ}\right) \cdot 2\left(\cos 10^{\circ}+i \sin 10^{\circ}\right) \) \( [?]\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \)
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