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

In summary, the terminal point P(-5,-2) in standard position has the exact values of csc=1/sin, sec=1/cos, and cot=1/tan. The signs for tan and cot depend on the quadrant the angle theta is in, with tan being positive in quadrant 1 and cot being positive in quadrant 3. Remembering this can be done through the acronym "CAST," but it is important to understand the signs instead of just memorizing them.
  • #1
Giu1iano
18
0

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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  • #2
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
  • #3
1488061120576.jpeg
 
  • #4
Check your signs on the tan and cot.
 
  • #5
Tan is y/x and Cot is x/y.. what's wrong with it?
 
  • #6
In what quadrants are tan and cot positive vs negative?
 
  • #7
1 and 3
 
  • #8
LCKurtz said:
In what quadrants are tan and cot positive vs negative?
Pos in quadrant 1 neg in quadrant 3
 
  • #9
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
 

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

1. What are the six trigonometric ratios for theta?

The six trigonometric ratios for theta are sine, cosine, tangent, cotangent, secant, and cosecant.

2. How do you find the exact values of the trigonometric ratios for theta?

To find the exact values of the trigonometric ratios for theta, you can use a calculator or reference a trigonometric table. Alternatively, you can use the Pythagorean identity and the values of the adjacent, opposite, and hypotenuse sides of a right triangle to calculate the ratios.

3. Can the values of the trigonometric ratios for theta be negative?

Yes, the values of the trigonometric ratios for theta can be negative, depending on the quadrant in which theta lies. For example, in quadrant II, only the sine and cosecant ratios are positive, while in quadrant III, only the tangent and cotangent ratios are positive.

4. Are there any special values for the trigonometric ratios of theta?

Yes, there are special values for certain angles of theta. For example, for theta = 0, the values of cosine and secant are both 1, and the values of sine and tangent are both 0. For theta = 30 degrees, the values of sine and cosecant are both 1/2, and the values of cosine and secant are both √3/2.

5. How are the trigonometric ratios for theta related to each other?

The trigonometric ratios for theta are related to each other through various identities and equations. For example, the Pythagorean identity states that sine squared plus cosine squared equals 1, and the reciprocal identities state that sine is equal to 1 over cosecant and cosine is equal to 1 over secant. These relationships can be used to find the value of one trigonometric ratio if the values of the others are known.

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