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Home Question Bank Math Trigonometry Archive 2024 November 30

Trigonometry Questions from Nov 30,2024

Browse the Trigonometry Q&A Archive for Nov 30,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Convert the angle from degrees to radians. 3. Solve \( \sin x=\frac{\sqrt{3}}{2} \), where \( 0 \leq x \leq 2 \pi \). a) How many solutions are possible? b) In which quadrants would you find the solutions? c) Determine the related acute angle for the equation. d) Determine all the solutions for the equation. A 26 - ft ladder leans against a building so that the angle between the ground and the ladder is \( 83^{\circ} \). How high does the ladder reach on the building? \( \frac { 2 \sin \theta + \cos \theta \theta - \frac { \sin \theta } { 1 - \cos \theta } } { 1 - \cos 2 \theta } \) \( 4 \tan x - 2 \operatorname { Cos } x = 2 \operatorname { cosec } x \) cable tower and a building are standing vertically on the same level ground. From the pe of the building which is 7 m high, the angle of elevation of the cable tower is \( 60^{\circ} \) and depression of its foot is \( 45^{\circ} \). Find the height of the tower. (Use \( \sqrt{3}=1.73 \) ) Solve the equation on the interval \( 0 \leq 0<2 \pi \) \( \sec \frac{3 \theta}{2}=-2 \) \( 1 \leftarrow \quad \) Solve the equation on the interval \( 0 \leq \theta<2 \pi \) \( \sec \frac{5 \theta}{4}=2 \) 3) Solve the following trigonometric equations within the domain \( [0,2 \pi] \). Round to the nearest tenth and use radians. a) \( 2 \sin ^{2} x-1=0 \) b) \( \csc ^{2} x+2 \csc x-3=0 \) c) \( \cos x-\cos 2 x=1 / 2 \) 2) Consider the function \( y=-4 \sin [4(x-\pi / 4)]+1 \) a) What is the amplitude? b) What is the period? c) Describe the phase shift. d) Describe the vertical translation. e) What is the domain and range of one cycle? f) Sketch one cycle of the function and label clearly all key features. Include an appropriate scale. g) Draw the exact function although model cosine on same grid.
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