these values right?

tan theta=2/3
sec theta=Squareroot(13)/3

sine=2xSquareroot(13)/13
Cos=3xSquareroot(13)/13
Tan=2/3
Cosecant=Square root (13)/2
Secant=Squareroot(3)/3
Cotangent=3/2

Yes, those values are correct. It seems like you have calculated the values of various trigonometric functions for a certain angle. Here is a breakdown of each value:

- tan(theta) = 2/3: This means that the tangent of the angle theta is equal to 2/3.
- sec(theta) = √13/3: This means that the secant of the angle theta is equal to the square root of 13 divided by 3.

Additionally, you have provided the values of sine, cosine, tangent, cosecant, secant, and cotangent for a specific angle. These values are based on the given angle:

- sine = 2√13/13: This means that the sine of the angle is equal to 2 multiplied by the square root of 13 divided by 13.
- cosine = 3√13/13: This means that the cosine of the angle is equal to 3 multiplied by the square root of 13 divided by 13.
- tangent = 2/3: This means that the tangent of the angle is equal to 2/3.
- cosecant = √13/2: This means that the cosecant of the angle is equal to the square root of 13 divided by 2.
- secant = √3/3: This means that the secant of the angle is equal to the square root of 3 divided by 3.
- cotangent = 3/2: This means that the cotangent of the angle is equal to 3/2.

It would be helpful if you provide the value of the angle for which you have calculated these values, as the exact angle determines these values.

Yes, these values are correct. The values you provided are the trigonometric ratios for the angle theta.

To find these values, you can use the definitions of the trigonometric functions and some basic trigonometric identities. Here's how you can get each of the values:

1. tan(theta) = 2/3:
You can find the value of theta by taking the inverse tangent (or arctan) of the given ratio: theta = arctan(2/3). Using a calculator, this would give you the angle in radians or degrees. For example, if you use degrees, you would get theta ≈ 33.69°.

2. sec(theta) = sqrt(13)/3:
Similarly, you can find the value of theta by taking the inverse secant (or arcsec) of the given ratio: theta = arcsec(sqrt(13)/3). Again, using a calculator, this would give you the angle in radians or degrees. For example, if you use degrees, you would get theta ≈ 38.7°.

3. sin(theta) = 2sqrt(13)/13:
You can find the value of sine by using the definition of sine: sin(theta) = opposite/hypotenuse. In this case, you can imagine a right triangle with an opposite side of length 2sqrt(13) and a hypotenuse of length 13. Dividing the opposite side by the hypotenuse gives you sin(theta) = 2sqrt(13)/13.

4. cos(theta) = 3sqrt(13)/13:
Similarly, you can find the value of cosine by using the definition of cosine: cos(theta) = adjacent/hypotenuse. In this case, you can imagine a right triangle with an adjacent side of length 3sqrt(13) and a hypotenuse of length 13. Dividing the adjacent side by the hypotenuse gives you cos(theta) = 3sqrt(13)/13.

5. csc(theta) = 2/sqrt(13):
The cosecant function is the reciprocal of the sine function: csc(theta) = 1/sin(theta). In this case, you can take the reciprocal of the sine value: csc(theta) = 1 / (2sqrt(13)/13) = 2/sqrt(13).

6. sec(theta) = sqrt(3)/3:
The secant function is the reciprocal of the cosine function: sec(theta) = 1/cos(theta). In this case, you can take the reciprocal of the cosine value: sec(theta) = 1 / (3sqrt(13)/13) = sqrt(3)/3.

7. cot(theta) = 3/2:
The cotangent function is the reciprocal of the tangent function: cot(theta) = 1/tan(theta). In this case, you can take the reciprocal of the tangent value: cot(theta) = 1 / (2/3) = 3/2.

Remember, these values can vary depending on the angle theta, so it's important to always specify the trigonometric ratio in the context of a particular angle.