Galifey wrote:1. Given 4x + 3y = 0 is the terminal side in quadrant II, the value of secθ = _____ (Answer should be an exact value written as a reduced fraction.)
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I can help you with the first question! I've attached a picture of the steps I took to reach the answer. The big purple numbers are the order in which you solve the question.
1. Convert 4x + 3y = 0 to y=mx+b form
2. Graph the line to find where it falls on the circle (this would be either quadrant 2 or 4, but it is given in the question so you use quadrant 2)
3.
a) Focus on the second quadrant and drop a perpendicular line to the x-axis so that you form a right triangle. Use the information given to fill in the side lengths. Use the pyhtagorean theorem to solve for the radius, or notice that it is a 3-4-5 triple
b) Use the formula for secant to find your answer (secθ=r/x) becomes (secθ=5/3)
c) Remember that because you are in the 2nd quadrant, only sine and cosecant are positive. Because we are finding sec, your answer must be negative
![20201105_100503.jpg](./download/file.php?id=380737&sid=e8029c6c1dfbcbf1d2c4a4bff487f5b2)
- 20201105_100503.jpg (214.01 KiB) Viewed 86 times
Hope this helped! It also has been a minute since I've done a problem like this, so be sure to double check my work!
Edit: just updated my answer with LostInTheEcho's correction. I fixed it on mobile so it's a bit messy, sorry!