Values of the six Trigonometric Functions

In summary, the values of the six trigonometric functions of an angle θ in standard position whose terminal side contains the point (-3,0) are: sinθ= 0, cosθ= -1, tanθ= 0, cscθ= undefined, secθ= -1, cotθ= undefined.
  • #1
MattO7766
2
0
Find the values of the six trigonometric functions of an angle θ in standard position whose terminal side is containing the points (-3,0)

Sinθ=
Cosθ=
Tanθ=
Cscθ=
Secθ=
Cotθ=

I believe the following are correct But I am not sure, Please give insight

Sinθ= 0/3
Cosθ= -3/3
Tanθ= 0/3
Cscθ= 3/0
Secθ= -3/3
Cotθ= 3/0
 
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  • #2
No, pretty much none of those are correct. I suggest you go back and check your basic definitions. The "circle" definition of the trig functions, which is what you appear to be using, requires that the terminal point be on the unit circle and (-3, 0) definitely is not- [itex](-3)^2+ (0)^2= 9[/itex], not 1. Of course, you can divide both -3 and 0 by 3 to get the point (-1, 0) which is on the same line through the origin and is on the unit circle.

Also, you should know that 0/a= 0 and that a/0 does not exist.
 
  • #3
First, the questions states that the point in question is P(-3, 0) only? So we are to assume that the origin is the starting point? But if that is the case, then all we have is a straight line down the negative x-axis. This would imply that the angle measured from the positive x-axis is simply [itex]\pi[/itex] or 180 degrees.

Is there another point that is given (your question states "pointS")?

Look here too: https://www.physicsforums.com/showthread.php?t=174661
 
Last edited:
  • #4
MattO7766 said:
Find the values of the six trigonometric functions of an angle θ in standard position whose terminal side is containing the points (-3,0)

Sinθ=
Cosθ=
Tanθ=
Cscθ=
Secθ=
Cotθ=

I believe the following are correct But I am not sure, Please give insight

Sinθ= 0/3
Cosθ= -3/3
Tanθ= 0/3
Cscθ= 3/0
Secθ= -3/3
Cotθ= 3/0

Sinθ= 0/3 = 0

Cosθ= -3/3 = -1

Tanθ= 0/3 = 0

Cscθ= 3/0

Secθ= -3/3 = -1

Cotθ= 3/0

What is 3/0 ?

The others are correct !
 

FAQ: Values of the six Trigonometric Functions

What are the six trigonometric functions?

The six trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. These functions represent the ratios of the sides of a right triangle, relative to one of its acute angles.

What is the unit circle and how is it related to trigonometric functions?

The unit circle is a circle with a radius of 1, centered at the origin (0,0) on a coordinate plane. The unit circle is used to define the values of trigonometric functions for any angle, not just acute angles. The x-coordinate of a point on the unit circle represents the cosine value and the y-coordinate represents the sine value for that angle.

How are trigonometric functions used in real life?

Trigonometric functions are used in various fields such as engineering, physics, and astronomy to solve problems involving angles and distances. They are also used in navigation, surveying, and construction to calculate angles and distances between points.

What are the key properties of trigonometric functions?

The key properties of trigonometric functions include periodicity, where the values of the functions repeat after a certain interval; symmetry, where the values of the functions are symmetric about the origin or a specific line; and even/odd functions, where the functions have specific properties when the input angle is positive or negative.

How can I find the values of trigonometric functions for special angles?

Special angles in trigonometry are angles that have simple and exact values for their trigonometric functions. These include 0°, 30°, 45°, 60°, and 90°, as well as their multiples. To find the values of trigonometric functions for these angles, you can use a unit circle, trigonometric identities, or a calculator.

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