State the exact values of all the trigonometric rations for theta.

AI Thread Summary
The discussion revolves around finding the exact values of all trigonometric ratios for angle theta, given the terminal point P(-5,-2). Participants emphasize the importance of correctly applying the formulas for sine, cosine, tangent, and their reciprocals, while also addressing the signs of these ratios based on the quadrant in which the angle lies. There is confusion regarding the signs of tangent and cotangent, with a reminder that tangent is positive in the third quadrant, contrary to initial claims. The conversation highlights the need for clarity in calculations and understanding of trigonometric principles. Ultimately, the thread concludes with a call for better explanation and understanding of the signs involved in trigonometric ratios.
Giu1iano
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Homework Statement


P(-5,-2) is a terminal point of angle theta in standard position. State the exact values of all the trigonometric rations for theta.

Homework Equations


x^2+y^2=r^2
csc=1/sin
sec=1/cos
cot=1/tan

The Attempt at a Solution


WIN_20170225_15_39_57_Pro.jpg
 
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Giu1iano said:

Homework Statement


P(-5,-2) is a terminal point of angle theta in standard position. State the exact values of all the trigonometric rations for theta.

Homework Equations


x^2+y^2=r^2
csc=1/sin
sec=1/cos
cot=1/tan

The Attempt at a Solution


View attachment 113737

Your image is unreadable. Please type out your solution.
 
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Likes Giu1iano
1488061120576.jpeg
 
Check your signs on the tan and cot.
 
Tan is y/x and Cot is x/y.. what's wrong with it?
 
In what quadrants are tan and cot positive vs negative?
 
1 and 3
 
LCKurtz said:
In what quadrants are tan and cot positive vs negative?
Pos in quadrant 1 neg in quadrant 3
 
Wrong. Look in your text.
 
  • #10
LCKurtz said:
Wrong. Look in your text.
Explain. I learn "CAST" to help remember that but first you explain
 
  • #11
I don't know or care what CAST is, but whatever it is you would do better to just understand the signs. What do you get if you calculate ##\tan \theta = \frac{-2}{-5}##?
 
  • #12
Perhaps you can find someone else to help you. I'm done.
 
  • #13
Closed for cleanup
 
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