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Tan 750 Degrees

The value of tan 750 degrees is 0.5773502. . .. Tan 750 degrees in radians is written as tan (750° × π/180°), i.e., tan (25π/6) or tan (13.089969. . .). In this article, we will discuss the methods to find the value of tan 750 degrees with examples.

Tan 750°: 1/√3
Tan 750° in decimal: 0.5773502. . .
Tan (-750 degrees): -0.5773502. . . or -1/√3
Tan 750° in radians: tan (25π/6) or tan (13.0899693 . . .)

What is the Value of Tan 750 Degrees?

The value of tan 750 degrees in decimal is 0.577350269. . .. Tan 750 degrees can also be expressed using the equivalent of the given angle (750 degrees) in radians (13.08996 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 750 degrees = 750° × (π/180°) rad = 25π/6 or 13.0899 . . .
∴ tan 750° = tan(13.0899) = 1/√3 or 0.5773502. . .

Explanation:

For tan 750°, the angle 750° > 360°. We can represent tan 750° as, tan(750° mod 360°) = tan(30°). The angle 750°, coterminal to angle 30°, is located in the First Quadrant(Quadrant I).
Since tangent function is positive in the 1st quadrant, thus tan 750 degrees value = 1/√3 or 0.5773502. . .
Similarly, given the periodic property of tan 750°, it can also be written as, tan 750 degrees = (750° + n × 180°), n ∈ Z.
⇒ tan 750° = tan 930° = tan 1110°, and so on.
Note: Since, tangent is an odd function, the value of tan(-750°) = -tan(750°).

Methods to Find Value of Tan 750 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 750° is given as 0.57735. . .. We can find the value of tan 750 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 750° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 750 degrees as:

sin(750°)/cos(750°)
± sin 750°/√(1 - sin²(750°))
± √(1 - cos²(750°))/cos 750°
± 1/√(cosec²(750°) - 1)
± √(sec²(750°) - 1)
1/cot 750°

Note: Since 750° lies in the 1st Quadrant, the final value of tan 750° will be positive.

We can use trigonometric identities to represent tan 750° as,

cot(90° - 750°) = cot(-660°)
-cot(90° + 750°) = -cot 840°
-tan (180° - 750°) = -tan(-570°)

Tan 750 Degrees Using Unit Circle

To find the value of tan 750 degrees using the unit circle, represent 750° in the form (2 × 360°) + 30° [∵ 750°>360°] ∵ The angle 750° is coterminal to 30° angle and also tangent is a periodic function, tan 750° = tan 30°.

Rotate ‘r’ anticlockwise to form 30° or 750° angle with the positive x-axis.
The tan of 750 degrees equals the y-coordinate(0.5) divided by x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of tan 750° = y/x = 0.5774 (approx).

☛ Also Check:

Examples Using Tan 750 Degrees

Example 1: Using the value of tan 750°, solve: (sec²(750°) - 1).

Solution:
We know, (sec²(750°) - 1) = (tan²(750°)) = 0.3333
⇒ (sec²(750°) - 1) = 0.3333
Example 2: Find the value of 6 tan(750°)/9 tan(-570°).

Solution:

Using trigonometric identities, we know, tan(750°) = -tan(180° - 750°) = -tan(-570°).
⇒ tan(750°) = -tan(-570°)
⇒ Value of 6 tan(750°)/9 tan(-570°) = -6/9 = -2/3
Example 3: Simplify: 9 (tan 750°/cot(-660°))

Solution:

We know tan 750° = cot(-660°)
⇒ 9 tan 750°/cot(-660°) = 9 (tan 750°/tan 750°)
= 9(1) = 9

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FAQs on Tan 750 Degrees

What is Tan 750 Degrees?

Tan 750 degrees is the value of tangent trigonometric function for an angle equal to 750 degrees. The value of tan 750° is 1/√3 or 0.5774 (approx).

What is the Value of Tan 750 Degrees in Terms of Cot 750°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 750° as 1/cot(750°). The value of cot 750° is equal to √3.

How to Find Tan 750° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 750° can be given in terms of other trigonometric functions as:

sin(750°)/cos(750°)
± sin 750°/√(1 - sin²(750°))
± √(1 - cos²(750°))/cos 750°
± 1/√(cosec²(750°) - 1)
± √(sec²(750°) - 1)
1/cot 750°

☛ Also check: trigonometric table

What is the Exact Value of tan 750 Degrees?

The exact value of tan 750 degrees can be given accurately up to 8 decimal places as 0.57735026 or as 1/√3.

How to Find the Value of Tan 750 Degrees?

The value of tan 750 degrees can be calculated by constructing an angle of 750° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of tan 750° is equal to the y-coordinate(0.5) divided by the x-coordinate (0.866). ∴ tan 750° = 1/√3 or 0.5774

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