Tan 7 Degrees
The value of tan 7 degrees is 0.1227845. . .. Tan 7 degrees in radians is written as tan (7° × π/180°), i.e., tan (0.122173. . .). In this article, we will discuss the methods to find the value of tan 7 degrees with examples.
- Tan 7° in decimal: 0.1227845. . .
- Tan (-7 degrees): -0.1227845. . .
- Tan 7° in radians: tan (0.1221730 . . .)
What is the Value of Tan 7 Degrees?
The value of tan 7 degrees in decimal is 0.122784560. . .. Tan 7 degrees can also be expressed using the equivalent of the given angle (7 degrees) in radians (0.12217 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 7 degrees = 7° × (π/180°) rad = 0.1221 . . .
∴ tan 7° = tan(0.1221) = 0.1227845. . .
Explanation:
For tan 7 degrees, the angle 7° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 7° value = 0.1227845. . .
Since the tangent function is a periodic function, we can represent tan 7° as, tan 7 degrees = tan(7° + n × 180°), n ∈ Z.
⇒ tan 7° = tan 187° = tan 367°, and so on.
Note: Since, tangent is an odd function, the value of tan(-7°) = -tan(7°).
Methods to Find Value of Tan 7 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 7° is given as 0.12278. . .. We can find the value of tan 7 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 7 Degrees Using Unit Circle
To find the value of tan 7 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 7° angle with the positive x-axis.
- The tan of 7 degrees equals the y-coordinate(0.1219) divided by x-coordinate(0.9925) of the point of intersection (0.9925, 0.1219) of unit circle and r.
Hence the value of tan 7° = y/x = 0.1228 (approx).
Tan 7° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 7 degrees as:
- sin(7°)/cos(7°)
- ± sin 7°/√(1 - sin²(7°))
- ± √(1 - cos²(7°))/cos 7°
- ± 1/√(cosec²(7°) - 1)
- ± √(sec²(7°) - 1)
- 1/cot 7°
Note: Since 7° lies in the 1st Quadrant, the final value of tan 7° will be positive.
We can use trigonometric identities to represent tan 7° as,
- cot(90° - 7°) = cot 83°
- -cot(90° + 7°) = -cot 97°
- -tan (180° - 7°) = -tan 173°
☛ Also Check:
Examples Using Tan 7 Degrees
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Example 1: Find the value of 2 tan 3.5°/(1 - tan²(3.5°)). [Hint: Use tan 7° = 0.1228]
Solution:
Using the tan 2a formula,
2 tan 3.5°/(1 - tan²(3.5°)) = tan(2 × 3.5°) = tan 7°
∵ tan 7° = 0.1228
⇒ 2 tan 3.5°/(1 - tan²(3.5°)) = 0.1228 -
Example 2: Simplify: 6 (tan 7°/cot 83°)
Solution:
We know tan 7° = cot 83°
⇒ 6 tan 7°/cot 83° = 6 (tan 7°/tan 7°)
= 6(1) = 6 -
Example 3: Find the value of 7 tan(7°)/10 tan(173°).
Solution:
Using trigonometric identities, we know, tan(7°) = -tan(180° - 7°) = -tan 173°.
⇒ tan(7°) = -tan(173°)
⇒ Value of 7 tan(7°)/10 tan(173°) = -7/10
FAQs on Tan 7 Degrees
What is Tan 7 Degrees?
Tan 7 degrees is the value of tangent trigonometric function for an angle equal to 7 degrees. The value of tan 7° is 0.1228 (approx).
How to Find the Value of Tan 7 Degrees?
The value of tan 7 degrees can be calculated by constructing an angle of 7° with the x-axis, and then finding the coordinates of the corresponding point (0.9925, 0.1219) on the unit circle. The value of tan 7° is equal to the y-coordinate(0.1219) divided by the x-coordinate (0.9925). ∴ tan 7° = 0.1228
How to Find Tan 7° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 7° can be given in terms of other trigonometric functions as:
- sin(7°)/cos(7°)
- ± sin 7°/√(1 - sin²(7°))
- ± √(1 - cos²(7°))/cos 7°
- ± 1/√(cosec²(7°) - 1)
- ± √(sec²(7°) - 1)
- 1/cot 7°
☛ Also check: trigonometry table
What is the Value of Tan 7 Degrees in Terms of Sin 7°?
Using trigonometric identities, we can write tan 7° in terms of sin 7° as, tan(7°) = sin 7°/√(1 - sin²(7°)) . Here, the value of sin 7° is equal to 0.1219.
What is the Value of Tan 7° in Terms of Cosec 7°?
Since the tangent function can be represented using the cosecant function, we can write tan 7° as 1/√(cosec²(7°) - 1). The value of cosec 7° is equal to 8.20550.
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