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Tan 70 Degrees

The value of tan 70 degrees is 2.7474774. . .. Tan 70 degrees in radians is written as tan (70° × π/180°), i.e., tan (7π/18) or tan (1.221730. . .). In this article, we will discuss the methods to find the value of tan 70 degrees with examples.

Tan 70° in decimal: 2.7474774. . .
Tan (-70 degrees): -2.7474774. . .
Tan 70° in radians: tan (7π/18) or tan (1.2217304 . . .)

What is the Value of Tan 70 Degrees?

The value of tan 70 degrees in decimal is 2.747477419. . .. Tan 70 degrees can also be expressed using the equivalent of the given angle (70 degrees) in radians (1.22173 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 70 degrees = 70° × (π/180°) rad = 7π/18 or 1.2217 . . .
∴ tan 70° = tan(1.2217) = 2.7474774. . .

Explanation:

For tan 70 degrees, the angle 70° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 70° value = 2.7474774. . .
Since the tangent function is a periodic function, we can represent tan 70° as, tan 70 degrees = tan(70° + n × 180°), n ∈ Z.
⇒ tan 70° = tan 250° = tan 430°, and so on.
Note: Since, tangent is an odd function, the value of tan(-70°) = -tan(70°).

Methods to Find Value of Tan 70 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 70° is given as 2.74747. . .. We can find the value of tan 70 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 70° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 70 degrees as:

sin(70°)/cos(70°)
± sin 70°/√(1 - sin²(70°))
± √(1 - cos²(70°))/cos 70°
± 1/√(cosec²(70°) - 1)
± √(sec²(70°) - 1)
1/cot 70°

Note: Since 70° lies in the 1st Quadrant, the final value of tan 70° will be positive.

We can use trigonometric identities to represent tan 70° as,

cot(90° - 70°) = cot 20°
-cot(90° + 70°) = -cot 160°
-tan (180° - 70°) = -tan 110°

Tan 70 Degrees Using Unit Circle

To find the value of tan 70 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 70° angle with the positive x-axis.
The tan of 70 degrees equals the y-coordinate(0.9397) divided by x-coordinate(0.342) of the point of intersection (0.342, 0.9397) of unit circle and r.

Hence the value of tan 70° = y/x = 2.7475 (approx).

☛ Also Check:

Examples Using Tan 70 Degrees

Example 1: Find the value of 8 tan(70°)/9 tan(110°).

Solution:

Using trigonometric identities, we know, tan(70°) = -tan(180° - 70°) = -tan 110°.
⇒ tan(70°) = -tan(110°)
⇒ Value of 8 tan(70°)/9 tan(110°) = -8/9
Example 2: Simplify: 3 (tan 70°/cot 20°)

Solution:

We know tan 70° = cot 20°
⇒ 3 tan 70°/cot 20° = 3 (tan 70°/tan 70°)
= 3(1) = 3
Example 3: Using the value of tan 70°, solve: (sec²(70°) - 1).

Solution:
We know, (sec²(70°) - 1) = (tan²(70°)) = 7.5486
⇒ (sec²(70°) - 1) = 7.5486

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FAQs on Tan 70 Degrees

What is Tan 70 Degrees?

Tan 70 degrees is the value of tangent trigonometric function for an angle equal to 70 degrees. The value of tan 70° is 2.7475 (approx).

How to Find Tan 70° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 70° can be given in terms of other trigonometric functions as:

sin(70°)/cos(70°)
± sin 70°/√(1 - sin²(70°))
± √(1 - cos²(70°))/cos 70°
± 1/√(cosec²(70°) - 1)
± √(sec²(70°) - 1)
1/cot 70°

☛ Also check: trigonometry table

What is the Value of Tan 70° in Terms of Cosec 70°?

Since the tangent function can be represented using the cosecant function, we can write tan 70° as 1/√(cosec²(70°) - 1). The value of cosec 70° is equal to 1.06417.

How to Find the Value of Tan 70 Degrees?

The value of tan 70 degrees can be calculated by constructing an angle of 70° with the x-axis, and then finding the coordinates of the corresponding point (0.342, 0.9397) on the unit circle. The value of tan 70° is equal to the y-coordinate(0.9397) divided by the x-coordinate (0.342). ∴ tan 70° = 2.7475

What is the Value of Tan 70 Degrees in Terms of Cot 70°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 70° as 1/cot(70°). The value of cot 70° is equal to 0.36397.

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