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MA1310: Module 3 Trigonometric Functions Exercise 3.2 Other Trigonometric Functions 1 Answer the following questions to complete this exercise: 1. The graph of a tangent function is given below. Find the equation of the graph in the form y = A tan ( Bx C ). a. Find A . The y-coordinate of the points on the graph 1 4 and 3 4 of the way between the consecutive asymptotes are given by –1 and 1 respectively. b. Find the period of the function (distance between two consecutive asymptotes). c. Find the coefficient of x , that is, B . d. Find the phase shift of the function (horizontal shift). e. Find the value of C . f. What is the correct equation of the given graph? Provide reasons. i. tan 2 yx     ii.   tan yx  iii.   tan yx   iv. tan 2 yx      2 2 4 4 x y
MA1310: Module 3 Trigonometric Functions Exercise 3.2 Other Trigonometric Functions 2 2. Find the exact value of: a. 1 3 sin 2 b. 1 3 cos 2     c. 1 tan 1 () d. 1 4 cos cos 3    e. 1 7 sin tan 24    3. Use the calculator to find the value of sin –1 0.47 to two decimal places. 4. Find the angle of elevation from the point on the ground 90 feet from the base of a building that is 200 feet tall. Submission Requirements: Submit your response in a Microsoft Word document of the following specifications: Font: Arial; Point 12 Spacing: Double Evaluation Criteria: Did you show the appropriate steps to solve the given problems? Did you support your answer with appropriate rationale wherever applicable? Were the answers submitted in an organized fashion that was legible and easy to follow? Were the answers correct?
MA1310: Module 4 Applications of Trigonometry Exercise 4.1 Laws of Sines and Cosines 1 48 97 12 A C a 1. Use the values given in the above triangle and find the value of B , b , and c . 2. Two sides and an angle (SSA) of a triangle are given. Determine if the given measurements produce one triangle, two triangles, or no triangle at all. a = 7, b = 5, A = 70°
MA1310: Module 4 Applications of Trigonometry Exercise 4.1 Laws of Sines and Cosines 2 3. You need to determine the distance between two points that lie on opposite banks of a river. The figure shows that 300 yards are measured along one bank. The angles from each end of this line segment to a point on the opposite bank are 620 and 530. Find the distance between A and B to the nearest tenth of a yard. 4. The diagram below shows three islands in Florida Bay. You rent a boat and plan to visit each of these remote islands. If you are on island B , on what bearing should you navigate to go to island C ? 5. Use Heron's formula to find the area of the triangle. Round off to the nearest square feet. a = 5 feet, b = 5 feet, c = 4 feet. Submission Requirements: Submit your response in a Microsoft Word document of the following specifications: Font: Arial; Point 12 Spacing: Double Evaluation Criteria: Did you show the steps to solve each problem? Did you write thorough explanations for the short-answer questions? Did you accurately choose a problem that fits the criteria for each rule? Island A Island C Island B 6 miles 5 miles 7 miles NW N
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MA1310: Module 4 Applications Of Trigonometry Exercise 4.2 Polar Coordinates and Complex Numbers 1 Answer the following questions to complete this exercise: 1. Explain why   r, and 180 r,     represent the same points in polar coordinates. 2. Match the point 4 2 ,     in polar coordinates with A , B , C , or D on the graph. 3. Find the rectangular coordinates of the polar point 5 5 2 ,    . 4. Find the polar coordinates of the rectangular point (–4, –4). 5. Plot the complex number 4 3 4 zi   and select the correct graph from the given graphs: a. b.
MA1310: Module 4 Applications Of Trigonometry Exercise 4.2 Polar Coordinates and Complex Numbers 2 c. d. 6. Find the absolute value of the complex number z = 2 + 5 i . 7. Write the complex number z = 2 – 2 i in polar form. Express in degrees. 8. Write the complex number 33 6 cos sin 22 i     in rectangular form. 9. Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. 5 1 cos sin 4 10 10 i        Submission Requirements: Submit your response in a Microsoft Word document of the following specifications: Font: Arial; Point 12 Spacing: Double
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MA1310: Module 3 Trigonometric Functions
Exercise 3.2
Other Trigonometric Functions
1.
(a) A=1
(b) The period of the function is the distance between two consecutive vertical
asymptotes. So the...

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