Tan 64 Degrees
The value of tan 64 degrees is 2.0503038. . .. Tan 64 degrees in radians is written as tan (64° × π/180°), i.e., tan (16π/45) or tan (1.117010. . .). In this article, we will discuss the methods to find the value of tan 64 degrees with examples.
- Tan 64° in decimal: 2.0503038. . .
- Tan (-64 degrees): -2.0503038. . .
- Tan 64° in radians: tan (16π/45) or tan (1.1170107 . . .)
What is the Value of Tan 64 Degrees?
The value of tan 64 degrees in decimal is 2.050303841. . .. Tan 64 degrees can also be expressed using the equivalent of the given angle (64 degrees) in radians (1.11701 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 64 degrees = 64° × (π/180°) rad = 16π/45 or 1.1170 . . .
∴ tan 64° = tan(1.1170) = 2.0503038. . .
Explanation:
For tan 64 degrees, the angle 64° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 64° value = 2.0503038. . .
Since the tangent function is a periodic function, we can represent tan 64° as, tan 64 degrees = tan(64° + n × 180°), n ∈ Z.
⇒ tan 64° = tan 244° = tan 424°, and so on.
Note: Since, tangent is an odd function, the value of tan(-64°) = -tan(64°).
Methods to Find Value of Tan 64 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 64° is given as 2.05030. . .. We can find the value of tan 64 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 64° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 64 degrees as:
- sin(64°)/cos(64°)
- ± sin 64°/√(1 - sin²(64°))
- ± √(1 - cos²(64°))/cos 64°
- ± 1/√(cosec²(64°) - 1)
- ± √(sec²(64°) - 1)
- 1/cot 64°
Note: Since 64° lies in the 1st Quadrant, the final value of tan 64° will be positive.
We can use trigonometric identities to represent tan 64° as,
- cot(90° - 64°) = cot 26°
- -cot(90° + 64°) = -cot 154°
- -tan (180° - 64°) = -tan 116°
Tan 64 Degrees Using Unit Circle
To find the value of tan 64 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 64° angle with the positive x-axis.
- The tan of 64 degrees equals the y-coordinate(0.8988) divided by x-coordinate(0.4384) of the point of intersection (0.4384, 0.8988) of unit circle and r.
Hence the value of tan 64° = y/x = 2.0503 (approx).
☛ Also Check:
FAQs on Tan 64 Degrees
What is Tan 64 Degrees?
Tan 64 degrees is the value of tangent trigonometric function for an angle equal to 64 degrees. The value of tan 64° is 2.0503 (approx).
What is the Value of Tan 64 Degrees in Terms of Sin 64°?
Using trigonometric identities, we can write tan 64° in terms of sin 64° as, tan(64°) = sin 64°/√(1 - sin²(64°)) . Here, the value of sin 64° is equal to 0.8988.
How to Find Tan 64° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 64° can be given in terms of other trigonometric functions as:
- sin(64°)/cos(64°)
- ± sin 64°/√(1 - sin²(64°))
- ± √(1 - cos²(64°))/cos 64°
- ± 1/√(cosec²(64°) - 1)
- ± √(sec²(64°) - 1)
- 1/cot 64°
☛ Also check: trigonometric table
How to Find the Value of Tan 64 Degrees?
The value of tan 64 degrees can be calculated by constructing an angle of 64° with the x-axis, and then finding the coordinates of the corresponding point (0.4384, 0.8988) on the unit circle. The value of tan 64° is equal to the y-coordinate(0.8988) divided by the x-coordinate (0.4384). ∴ tan 64° = 2.0503
What is the Value of Tan 64° in Terms of Sec 64°?
We can represent the tangent function in terms of the secant function using trig identities, tan 64° can be written as √(sec²(64°) - 1). Here, the value of sec 64° is equal to 2.2811.