Trigonometry Homework Help

. Determine the exact value of each trigonometric ratio. Rationalize all ratios. \text { d) } \cos \left(\frac{25 \pi}{6}\right) \text { b) } \tan \left(60^{\circ}\right) \text { c) } \cos \left(-\frac{5 \pi}{4}\right) \text { d) } \cot \left(-120^{\circ}\right)

\text { Determile a negative co-terminal angle, in degrees, with } \theta=\frac{4 \pi}{5} \text {. }

Question 3 Example 4.22. The angle of elevation from a boat at P to a point T, at the top of a vertical cliff is measured to be 30°. The boat sails 1000 metres to a second point Q, from which the angle of elevation to T is measured to be 45°. Let R be the point at the base of the cliff directly below 7 and let h be the height of this cliff. The bearings of R from P and Q are 050ºT and 310ºT respectively. a) Draw a diagram expressing all this information. b) Show that ZPRQ = 100°. 1000² c) Show that h²= 4+2√3 sin 10° d) Hence evaluate the height of the cliff correct to the nearest metre.

3. Determine the EXACT value of cos45°(1 - sec30°) using your special triangles. Simplify fully. Show all work to receive process marks. Ⓒ

4. The boom of a crane can be moved so that its angle of inclination changes. In one location, close to some buildings and some overhead power cables, the minimum value of the angle of inclination is 30°, and the maximum value is 60°. If the boom is 10 m long, find the vertical displacement of the end of the boom when the angle of inclination increases from its minimum value to its maximum value. a) Express your answer in EXACT form using your special triangles. Show all work to receive process marks. Ⓒ b) Express your answer in approximate form, to the nearest tenth of a metre. УА 10 m 60° 30° vertical displacement Уг 10 m x

5. Given angle 0, where 0° ≤ 0 ≤ 360°, determine two possible values of 0, to the nearest degree, where the following ratio would be true. Sketch both principal angles and label them using a diagram. Ⓒ tane = -0.9598

6. Determine the number of possible triangles that could be drawn with the given measures. Only determine the height when needed. Fill in the table with your information. DO NOT SOLVE.Ⓡ Measures Height Given APQR, LP = 114°, p = 16, q = 28 Given ADEF, LE = 53°, ƒ = 10.7, e = 7.1 Given AJKL, ZK = 44°, l = 13.6, k = 9.4 Given AXYZ, ZX = 137°, x = 18.5, y = 6.2 Given AABC, LB = 28°, c = 18, b = 11 Number of Possible Triangles

7. The point P(-5, -12) lies on the terminal arm of an angle in standard position. Determine the trig ratios for sine, cose and cote. Then find to the nearest degree. Include a fully labeled diagram. Ⓒ +

10. A light in a park can illuminate effectively up to a distance of 100 m. A point on a bike path is 150 m from the light. The sight line to the light makes an angle of 23° with the bike path. What length of the bike path, to the nearest metre, is effectively illuminated by the light? Show all steps to receive process marks. 23° 150 m Bike Path

11. To measure the height, CD, of an inaccessible cliff, a surveyor recorded the data shown. Find the height of the cliff, to the nearest tenth of a metre. Ⓒ Show all steps to receive process marks. A 38° D 50 m 61° 72° B

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14. A cyclist travels west for 6 miles, makes a right turn and travels north for 4 miles. What is the bearing from the starting point to the cyclist's current position? Round your angle to two decimal places. [5 points] Draw a picture representing the situation and show all steps leading to your answer.

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2. Graph f(x) = x sinx on [-4, 4π] and verbalize how the graph varies from the graphs of f(x) = ±x. sin r x Graph f(x) = on the window [-51, 5π] and describe freely what the graph shows. You can use www.desmos.com/calculator to obtain the graphs.

Reflect on the concepts of trigonometry. What concepts (only the names) did you need to accommodate the concepts of trigonometry in your mind? What are the simplest trigonometry concepts you can imagine? In your day to day, is there any occurring fact that can be interpreted as periodic patterns? What strategy are you using to get the graphs of trigonometric functions? Abramson, J. (2021). Algebra and trigonometry (2nd ed.). OpenStax, TX: Rice University. Retrieved from https://openstax.org/details/books/algebra-and-trigonometry-2e Read the following sections in Chapters 7 and 8: Section 7.1 Angles Section 7.2 Right Triangle Trigonometry Section 7.3 Unit Circle Section 8.1 Graphs of the Sine and Cosine Functions Section 8.2 Graphs of the Other Trigonometric Functions Section 8.3 Inverse Trigonometric Functions Need to do in 200 words, 7th edition APA CITATION FORMAT

5.) Kerri is flying a kite that is on a 100 foot string. The angle of elevation from the ground to the top of the kite is 52 degrees. How high is the kite off the ground? (2 points) 100 52