Trignometry assignment

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Challenge Problems 1. Be sure to attach a hand - sketch for this problem. (a) First draw −𝟐𝟐𝟐𝟐𝟐𝟐° in standard position. (b) Now draw the reference angle of −𝟐𝟐𝟐𝟐𝟐𝟐° in the same diagram. Do not find the value, just draw it. Remember the definition: The reference angle of a given angle is the POSITIVE ACUTE angle formed by the terminal side of the angle and the NEAREST x – axis. (c) Use the drawing in part (b) to find the value of the reference angle. 2. Find the exact value of the following expression which basically stands for the sum of cos 1° , cos 2° , cos 3° all the way up to cos 179°. Do not use a calculator. cos 1° + cos 2° + cos 3° + ⋯ ⋯ ⋯ + cos 178° + cos 179° Hints: See the hints below. i. ii. Start by establishing a relationship between the last term cos 179° and the first term cos 1°. To establish the relationship, first draw 179° in standard position and find its reference angle. Then use the reference angle and the quadrant in which 179° lies to rewrite cos 179° in terms of cos 1°. This will help you evaluate cos 1° + cos 179°. Follow the above method to evaluate the intermediate sums cos 2° + cos 178°, cos 3° + cos 177° and so on. 3. A person's blood pressure follows a sine wave corresponding to the beats of the heart. A particular individual's blood pressure at time t (measured in minutes) is P (t) = 20 sin(160𝜋𝜋𝜋𝜋) + 110. What does this tell us about the person's (a) heart rate, (b) systolic and diastolic blood pressure? 1 4. Determine the amplitude, period, and phase shift for the function 𝑦𝑦 = 𝜋𝜋 cos(𝜋𝜋 𝑥𝑥 − Then graph one period of the function using a graphing utility such as Graphmatica, Desmos or something of your choice. Hand sketches will not be accepted. 1 3 ). Note: Some graphing tips can be found in the “Math Calculator and Graphing Resources” page under the “Course Specific Information” module.
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Hi Please check the attached file for details, let me know if you have any question, thank you. Best, James


b. The reference angle of -245 is marked red.
c. the value of refer...

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