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 HW #11 (due Wed Dec 7) & Exam 3 Review
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December 2, 2016 at 10:28 am #40406
The exercises for this HW are all from the Final Exam Review sheet (you should have already downloaded the pdf, from “Files” or http://www.citytech.cuny.edu/mathematics/docs/review/MAT1275FinalRview.pdf).
The questions on Exam 3 will be very similar to these exercises, so please work through these exercises!
Here is the list of exercises to do, along with some hints:
#8: Finding the values of the 5 remaining trig functions based on the value of one trig function (and information about the sign of one other trig function):
 For these exercises, first use the given info to identify which quadrant the angle theta must be in, and then draw a triangle
 See the examples we did in class, and also Example #5 in Sec 1.3 (p26) of the Trigonometry textbook
#9: Using the Law of Sines or Law of Cosines to solve for a certain side or angle in a triangle:
 We will cover this material and go through some examples on Monday
 If possible, read ahead in Sec 7.1 (Example 1, pp317318) and Sec 7.2 (Examples 2 & 3, pp331332)
#10: Verifying Trig Identities–use the fundamental trig identities (listed in Sec 1.4) and algebra to show the LHS is equal to the RHS of the given identity:
 See the example we did in class on Wednesday
 See also Sec 1.4, Examples 24 (pp3233); and Sec 5.1, Examples 1 & 2 (pp212213)
#11: Solving Trig Equations
 FIrst do some simple algebra to put the given equation in the form “trig function = a number”
 then use the unit circle to find the angle(s)
 You can use this image of the unit circle for reference: https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/1000pxUnit_circle_angles_color.svg.png
 This topic was modified 3 years ago by Suman Ganguli.
 This topic was modified 2 years, 12 months ago by Suman Ganguli.
December 6, 2016 at 12:14 pm #40441Below are some additional notes and hints on these Final Exam Review exercises, based on our discussion in class yesterday.
Some general advice: If you get stuck on any of these exercises, start by reviewing the similar examples we did in class and the similar textbook examples (which I’ve listed for you). If you’re still stuck, it can be helpful to look at the solution and try to work out how to get to that solution.)
#8: As listed above, look at Example #5 in Sec 1.3 (p26) of the Trigonometry textbook. See also the box “Trigonometric Functions of Any Angle” on p25 of the textbook. For the initial step of figuring out which quadrant the angle is in, you’ll need to know which trig functions are positive in which quadrant: “All” in Q1, sin in Q2, tan in Q3, and cos in Q4.
#9: For parts (a) and (c), use the Law of Cosines, and for parts (b) and (d) use the Law of Sines. Again, look at the examples listed above, from Sections 7.1 and 7.2. Those sections also list the Law of Sines and Law of Cosines, respectively.
(But note that solving part (a) involves the “inverse cosine” function. You can use the Law of Cosines to eventually get the equation “cos C = 0.953125”–you should write up how to get that! Then, in order to then solve for the angle C, you need to use the inverse cosine function using a scientific calculator, which outputs the angle (between 0 and 180 degrees) which has the input number as its cosine. For example, on the Google calculator, you hit the “Inv” button (which changes to the cos button to cos^(1), to represent the inverse function), then hit “cos^(1)”, then input 0.953125. This returns 17.6 degrees, which is the solution to the exercise.
Tomorrow’s exam will not have a question that involves using inverse cosine or inverse sine, but it’s good practice to understand how to set it up using the Laws. Look in particular at Example 3 on pp331332.)
#10: For the trig identity proofs, if you’re not sure how to approach these, it can be helpful to study the solutions and figure out exactly what is happening at each step!
Also, it’s useful for these to have the fundamental trig identities in front of you. They are listed in the box on p212 of the textbook (you can ignore the “Identities due to symmetry”), and they are also summarized on the top half of this pdf:
https://www.coastal.edu/mathcenter/HelpPages/Handouts/trident.PDFYou don’t have to memorize the identities! I will provide them to you for the exam.

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