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Tan 73 Degrees

The value of tan 73 degrees is 3.2708526. . .. Tan 73 degrees in radians is written as tan (73° × π/180°), i.e., tan (1.274090. . .). In this article, we will discuss the methods to find the value of tan 73 degrees with examples.

Tan 73° in decimal: 3.2708526. . .
Tan (-73 degrees): -3.2708526. . .
Tan 73° in radians: tan (1.2740903 . . .)

What is the Value of Tan 73 Degrees?

The value of tan 73 degrees in decimal is 3.270852618. . .. Tan 73 degrees can also be expressed using the equivalent of the given angle (73 degrees) in radians (1.27409 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 73 degrees = 73° × (π/180°) rad = 1.2740 . . .
∴ tan 73° = tan(1.2740) = 3.2708526. . .

Explanation:

For tan 73 degrees, the angle 73° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 73° value = 3.2708526. . .
Since the tangent function is a periodic function, we can represent tan 73° as, tan 73 degrees = tan(73° + n × 180°), n ∈ Z.
⇒ tan 73° = tan 253° = tan 433°, and so on.
Note: Since, tangent is an odd function, the value of tan(-73°) = -tan(73°).

Methods to Find Value of Tan 73 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 73° is given as 3.27085. . .. We can find the value of tan 73 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 73° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 73 degrees as:

sin(73°)/cos(73°)
± sin 73°/√(1 - sin²(73°))
± √(1 - cos²(73°))/cos 73°
± 1/√(cosec²(73°) - 1)
± √(sec²(73°) - 1)
1/cot 73°

Note: Since 73° lies in the 1st Quadrant, the final value of tan 73° will be positive.

We can use trigonometric identities to represent tan 73° as,

cot(90° - 73°) = cot 17°
-cot(90° + 73°) = -cot 163°
-tan (180° - 73°) = -tan 107°

Tan 73 Degrees Using Unit Circle

To find the value of tan 73 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 73° angle with the positive x-axis.
The tan of 73 degrees equals the y-coordinate(0.9563) divided by x-coordinate(0.2924) of the point of intersection (0.2924, 0.9563) of unit circle and r.

Hence the value of tan 73° = y/x = 3.2709 (approx).

☛ Also Check:

Examples Using Tan 73 Degrees

Example 1: Using the value of tan 73°, solve: (sec²(73°) - 1).

Solution:
We know, (sec²(73°) - 1) = (tan²(73°)) = 10.6985
⇒ (sec²(73°) - 1) = 10.6985
Example 2: Find the value of (2 sin (36.5°) cos (36.5°) sec (73°)). [Hint: Use tan 73° = 3.2709]

Solution:

Using sin 2a formula,
2 sin (36.5°) cos (36.5°) = sin (2 × 36.5°) = sin 73°
⇒ 2 sin (36.5°) cos (36.5°) sec(73°) = sin 73° sec 73°
= sin 73°/cos 73° = tan 73°
⇒ (2 sin (36.5°) cos (36.5°) sec(73°)) = 3.2709
Example 3: Simplify: 4 (tan 73°/cot 17°)

Solution:

We know tan 73° = cot 17°
⇒ 4 tan 73°/cot 17° = 4 (tan 73°/tan 73°)
= 4(1) = 4

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FAQs on Tan 73 Degrees

What is Tan 73 Degrees?

Tan 73 degrees is the value of tangent trigonometric function for an angle equal to 73 degrees. The value of tan 73° is 3.2709 (approx).

How to Find the Value of Tan 73 Degrees?

The value of tan 73 degrees can be calculated by constructing an angle of 73° with the x-axis, and then finding the coordinates of the corresponding point (0.2924, 0.9563) on the unit circle. The value of tan 73° is equal to the y-coordinate(0.9563) divided by the x-coordinate (0.2924). ∴ tan 73° = 3.2709

What is the Value of Tan 73 Degrees in Terms of Cot 73°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 73° as 1/cot(73°). The value of cot 73° is equal to 0.30573.

What is the Value of Tan 73° in Terms of Sec 73°?

We can represent the tangent function in terms of the secant function using trig identities, tan 73° can be written as √(sec²(73°) - 1). Here, the value of sec 73° is equal to 3.4203.

How to Find Tan 73° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 73° can be given in terms of other trigonometric functions as:

sin(73°)/cos(73°)
± sin 73°/√(1 - sin²(73°))
± √(1 - cos²(73°))/cos 73°
± 1/√(cosec²(73°) - 1)
± √(sec²(73°) - 1)
1/cot 73°

☛ Also check: trigonometry table

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