Tan 145 Degrees
The value of tan 145 degrees is -0.7002075. . .. Tan 145 degrees in radians is written as tan (145° × π/180°), i.e., tan (29π/36) or tan (2.530727. . .). In this article, we will discuss the methods to find the value of tan 145 degrees with examples.
- Tan 145° in decimal: -0.7002075. . .
- Tan (-145 degrees): 0.7002075. . .
- Tan 145° in radians: tan (29π/36) or tan (2.5307274 . . .)
What is the Value of Tan 145 Degrees?
The value of tan 145 degrees in decimal is -0.700207538. . .. Tan 145 degrees can also be expressed using the equivalent of the given angle (145 degrees) in radians (2.53072 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 145 degrees = 145° × (π/180°) rad = 29π/36 or 2.5307 . . .
∴ tan 145° = tan(2.5307) = -0.7002075. . .
Explanation:
For tan 145 degrees, the angle 145° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 145° value = -0.7002075. . .
Since the tangent function is a periodic function, we can represent tan 145° as, tan 145 degrees = tan(145° + n × 180°), n ∈ Z.
⇒ tan 145° = tan 325° = tan 505°, and so on.
Note: Since, tangent is an odd function, the value of tan(-145°) = -tan(145°).
Methods to Find Value of Tan 145 Degrees
The tangent function is negative in the 2nd quadrant. The value of tan 145° is given as -0.70020. . .. We can find the value of tan 145 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 145° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 145 degrees as:
- sin(145°)/cos(145°)
- ± sin 145°/√(1 - sin²(145°))
- ± √(1 - cos²(145°))/cos 145°
- ± 1/√(cosec²(145°) - 1)
- ± √(sec²(145°) - 1)
- 1/cot 145°
Note: Since 145° lies in the 2nd Quadrant, the final value of tan 145° will be negative.
We can use trigonometric identities to represent tan 145° as,
- cot(90° - 145°) = cot(-55°)
- -cot(90° + 145°) = -cot 235°
- -tan (180° - 145°) = -tan 35°
Tan 145 Degrees Using Unit Circle
To find the value of tan 145 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 145° angle with the positive x-axis.
- The tan of 145 degrees equals the y-coordinate(0.5736) divided by x-coordinate(-0.8192) of the point of intersection (-0.8192, 0.5736) of unit circle and r.
Hence the value of tan 145° = y/x = -0.7002 (approx).
☛ Also Check:
FAQs on Tan 145 Degrees
What is Tan 145 Degrees?
Tan 145 degrees is the value of tangent trigonometric function for an angle equal to 145 degrees. The value of tan 145° is -0.7002 (approx).
How to Find Tan 145° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 145° can be given in terms of other trigonometric functions as:
- sin(145°)/cos(145°)
- ± sin 145°/√(1 - sin²(145°))
- ± √(1 - cos²(145°))/cos 145°
- ± 1/√(cosec²(145°) - 1)
- ± √(sec²(145°) - 1)
- 1/cot 145°
☛ Also check: trigonometry table
What is the Value of Tan 145 Degrees in Terms of Sin 145°?
Using trigonometric identities, we can write tan 145° in terms of sin 145° as, tan(145°) = -sin 145°/√(1 - sin²(145°)) . Here, the value of sin 145° is equal to 0.5736.
What is the Value of Tan 145° in Terms of Sec 145°?
We can represent the tangent function in terms of the secant function using trig identities, tan 145° can be written as -√(sec²(145°) - 1). Here, the value of sec 145° is equal to -1.2207.
How to Find the Value of Tan 145 Degrees?
The value of tan 145 degrees can be calculated by constructing an angle of 145° with the x-axis, and then finding the coordinates of the corresponding point (-0.8192, 0.5736) on the unit circle. The value of tan 145° is equal to the y-coordinate(0.5736) divided by the x-coordinate (-0.8192). ∴ tan 145° = -0.7002