ratio of the length of the opposite leg to the length of the hypotenuse. Cosine (cos) Function of an acute angle of a right triangle is equal to the ratio of the length of the adjacent leg to the length of the hypotenuse. Tangent (tan) Function is equal to the ratio of the length of the opposite leg to the length of the adjacent leg. The reciprocal of the sine function is the Cosecant (csc) Function. The reciprocal of cosine and tangent are Secant (sec) and Cotangent (cot) function respectively.
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Right Triangle Trigonometry Trigonometry is a branch of mathematics involving the study of triangles‚ and has applications in fields such as engineering‚ surveying‚ navigation‚ optics‚ and electronics. Also the ability to use and manipulate trigonometric functions is necessary in other branches of mathematics‚ including calculus‚ vectors and complex numbers. Right-angled Triangles In a right-angled triangle the three sides are given special names. The side opposite the right angle is called the
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horizontal translation for the function C=2 8. If a bicycle wheel makes 7 rotations a second and has a diameter of 75 cm‚ what cosine function describes the height of a point on the end of the wheel? T=3 9. What is the amplitude of the function ? C=1 10. What adjustment is needed to change the cosine function to the sine function? C=1 11. The height of a swing is modelled by the function . What are the highest and lowest
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three terms. 6. Consider the sequence 16‚ –8‚ 4‚ –2‚ 1‚ ... a. Describe the pattern formed in the sequence. b. Find the next three terms. 7. Consider the graph of the cosine function shown below. a. Find the period and amplitude of the cosine function. b. At what values of for do the maximum value(s)‚ minimum values(s)‚ and zeros occur? Verify the identity. Justify each step. 8. sinΘ/cosΘ+cosΘ/sinΘ sin^20+cos^2Θ/sinΘcosΘ
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of 6 cm‚ find the area of the shaded region. cQ4. The diagram shows a circle‚ centre O‚ with a radius 12 cm. The chord AB subtends at an angle of 75° at the centre. The tangents to the circle at A and B meet at P. (a) Using the cosine rule‚ show that the length of AB is (b) Find the length of BP. (c) Hence find (i) the area of triangle OBP; (ii) the area of triangle ABP. (d) Find the area of sector OAB. (e) Find the area
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RIGHT TRIANGLE TRIGONOMETRY The word Trigonometry can be broken into the parts Tri‚ gon‚ and metry‚ which means “Three angle measurement‚” or equivalently “Triangle measurement.” Throughout this unit‚ we will learn new ways of finding missing sides and angles of triangles which we would be unable to find using the Pythagorean Theorem alone. The basic trigonometric theorems and definitions will be found in this portion of the text‚ along with a few examples‚ but the reader will frequently
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Pythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I ’ll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion‚ a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears
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Applied Mathematics 1 Trigonometric Ratios with solutions O A O cos θ = tan θ = H H A where O = opposite‚ A = adjacent and H = hypotenuse. sin θ = 1. The angle of elevation of the top of a tree from a point on the ground 10m from the base of the tree is 28◦ . What is the height of the tree? Solution We need to find the height of tree which is opposite an angle of 28◦ .Thus O tan θ = A O = A tan θ height of tree = 10 × tan 28◦ =⇒ height of tree = 5.3m 1d.p. 2. Using a surveying
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MAT 117 /MAT117 Course Algebra 1B MAT 117 /MAT117 Week 6 Discussion Question Version 8 Week 6 DQ 2 1. Other than those listed in the text‚ how might the Pythagorean theorem be used in everyday life? 2. Provide examples of each. RESPONSE 1. Other than those listed in the text‚ how might the Pythagorean theorem be used in everyday life? Well other than the way its listed in the text the way that the pythagorean theorem can be used any time is when we have a right triangle
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Trigonometry is… i) A ration shows approximate sizes of two or more values. Ratios can be shown in different ways. For example 1:3 (one to three)‚ ¼ (one fourth). ii) * Sine (θ) = Opposite x Hypotunese-1 * Cosine (θ) = Adjacent x Hypotunese-1 * Tangent (θ) = Opposite x Adjacent -1 iii) You can remember this equations throughout a word SohCahToa Trigonometry came from… i) The term “trigonometry‚” although not of native Greek origin‚ comes from the Greek word trigonon
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