Which Of The Following Is Equivalent To Tan 5pi 6?
Tan 5pi/6 is equivalent to -sqrt(3)/3. Finding the equivalent value of tan 5pi/6 involves understanding trigonometric functions. Tan represents the ratio of the opposite side to the adjacent side in a right triangle. In this case, 5pi/6 falls in the second quadrant. The negative sign indicates the direction of the angle. By using the unit circle or reference angles, we can determine the exact value. Knowing the values of sin and cos for 5pi/6 is essential in calculating tan. Remembering the special triangles and angles can also aid in simplifying the process. With practice and familiarity with trigonometric identities, finding the equivalent value of tan 5pi/6 becomes more manageable.
Contents
| Tan 5pi/6 is equivalent to -√3 / 3. |
| It is also equal to -√3 / 3. |
| The reference angle for 5pi/6 is pi/6. |
| Tan 5pi/6 falls in the third quadrant. |
| The exact value of tan 5pi/6 is -√3 / 3. |
- 5pi/6 is equivalent to 150 degrees in degrees.
- The periodicity of the tangent function is pi.
- 5pi/6 is in the angle range of 90 to 180 degrees.
- The reciprocal of tangent is cotangent.
- Tan 5pi/6 can also be written as -√3 / 3.
What is the value of tan(5π/6)?
Tan of 5π/6 is equivalent to the negative square root of 3. It represents the ratio of the sine to the cosine of the given angle.
- Tan(5π/6) = -√3
- Tan(5π/6) = -1.732
How can tan(5π/6) be expressed in degrees?
The value of tan(5π/6) can be converted to degrees by multiplying the given radians by 180/π. This conversion results in approximately -150 degrees.
| Tan(5π/6) in degrees | -150° |
What is the relationship between tan(5π/6) and the unit circle?
The value of tan(5π/6) on the unit circle corresponds to the y-coordinate of the point where the terminal side of the angle intersects the unit circle.
- Unit circle point: (-1/2, -√3/2)
Is tan(5π/6) a positive or negative value?
Tan(5π/6) is a negative value since the angle falls in the second quadrant where tan is negative.
| Tan(5π/6) | Negative |
How does tan(5π/6) relate to the reference angle?
The reference angle for 5π/6 is π/6. Since 5π/6 is in the second quadrant, the reference angle helps determine the relationship of tan(5π/6) with the positive x-axis.
- Reference angle: π/6
What is the reciprocal identity of tan(5π/6)?
The reciprocal identity of tan(5π/6) is the cotangent of the same angle. It is the reciprocal of the tangent function.
| Cot(5π/6) | -√3/3 |
How does tan(5π/6) compare to other trigonometric functions?
When compared to other trigonometric functions like sine and cosine, tan(5π/6) has a unique value that represents the slope of the angle in the coordinate plane.
- Tan(5π/6) vs. Sine and Cosine
What is the periodicity of tan(5π/6)?
The periodicity of tan(5π/6) is π since the tangent function repeats its values every π radians.
| Periodicity of Tan(5π/6) | π |
How can tan(5π/6) be represented geometrically?
Geometrically, tan(5π/6) can be represented as the slope of a line passing through the point on the unit circle corresponding to the angle.
- Geometric Representation of Tan(5π/6)