A day full of math games & activities. Find one near you.

Tan 67 Degrees

The value of tan 67 degrees is 2.3558523. . .. Tan 67 degrees in radians is written as tan (67° × π/180°), i.e., tan (1.169370. . .). In this article, we will discuss the methods to find the value of tan 67 degrees with examples.

Tan 67° in decimal: 2.3558523. . .
Tan (-67 degrees): -2.3558523. . .
Tan 67° in radians: tan (1.1693705 . . .)

What is the Value of Tan 67 Degrees?

The value of tan 67 degrees in decimal is 2.355852365. . .. Tan 67 degrees can also be expressed using the equivalent of the given angle (67 degrees) in radians (1.16937 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 67 degrees = 67° × (π/180°) rad = 1.1693 . . .
∴ tan 67° = tan(1.1693) = 2.3558523. . .

Explanation:

For tan 67 degrees, the angle 67° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 67° value = 2.3558523. . .
Since the tangent function is a periodic function, we can represent tan 67° as, tan 67 degrees = tan(67° + n × 180°), n ∈ Z.
⇒ tan 67° = tan 247° = tan 427°, and so on.
Note: Since, tangent is an odd function, the value of tan(-67°) = -tan(67°).

Methods to Find Value of Tan 67 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 67° is given as 2.35585. . .. We can find the value of tan 67 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 67° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 67 degrees as:

sin(67°)/cos(67°)
± sin 67°/√(1 - sin²(67°))
± √(1 - cos²(67°))/cos 67°
± 1/√(cosec²(67°) - 1)
± √(sec²(67°) - 1)
1/cot 67°

Note: Since 67° lies in the 1st Quadrant, the final value of tan 67° will be positive.

We can use trigonometric identities to represent tan 67° as,

cot(90° - 67°) = cot 23°
-cot(90° + 67°) = -cot 157°
-tan (180° - 67°) = -tan 113°

Tan 67 Degrees Using Unit Circle

To find the value of tan 67 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 67° angle with the positive x-axis.
The tan of 67 degrees equals the y-coordinate(0.9205) divided by x-coordinate(0.3907) of the point of intersection (0.3907, 0.9205) of unit circle and r.

Hence the value of tan 67° = y/x = 2.3559 (approx).

☛ Also Check:

Examples Using Tan 67 Degrees

Example 1: Find the value of 2 tan(67°)/10 tan(113°).

Solution:

Using trigonometric identities, we know, tan(67°) = -tan(180° - 67°) = -tan 113°.
⇒ tan(67°) = -tan(113°)
⇒ Value of 2 tan(67°)/10 tan(113°) = -2/10 = -1/5
Example 2: Simplify: 9 (tan 67°/cot 23°)

Solution:

We know tan 67° = cot 23°
⇒ 9 tan 67°/cot 23° = 9 (tan 67°/tan 67°)
= 9(1) = 9
Example 3: Find the value of (2 sin (33.5°) cos (33.5°) sec (67°)). [Hint: Use tan 67° = 2.3559]

Solution:

Using sin 2a formula,
2 sin (33.5°) cos (33.5°) = sin (2 × 33.5°) = sin 67°
⇒ 2 sin (33.5°) cos (33.5°) sec(67°) = sin 67° sec 67°
= sin 67°/cos 67° = tan 67°
⇒ (2 sin (33.5°) cos (33.5°) sec(67°)) = 2.3559

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Tan 67 Degrees

What is Tan 67 Degrees?

Tan 67 degrees is the value of tangent trigonometric function for an angle equal to 67 degrees. The value of tan 67° is 2.3559 (approx).

What is the Value of Tan 67 Degrees in Terms of Cot 67°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 67° as 1/cot(67°). The value of cot 67° is equal to 0.42447.

What is the Value of Tan 67° in Terms of Sec 67°?

We can represent the tangent function in terms of the secant function using trig identities, tan 67° can be written as √(sec²(67°) - 1). Here, the value of sec 67° is equal to 2.5593.

How to Find the Value of Tan 67 Degrees?

The value of tan 67 degrees can be calculated by constructing an angle of 67° with the x-axis, and then finding the coordinates of the corresponding point (0.3907, 0.9205) on the unit circle. The value of tan 67° is equal to the y-coordinate(0.9205) divided by the x-coordinate (0.3907). ∴ tan 67° = 2.3559

How to Find Tan 67° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 67° can be given in terms of other trigonometric functions as:

sin(67°)/cos(67°)
± sin 67°/√(1 - sin²(67°))
± √(1 - cos²(67°))/cos 67°
± 1/√(cosec²(67°) - 1)
± √(sec²(67°) - 1)
1/cot 67°

☛ Also check: trigonometric table

Download FREE Study Materials

Trigonometry

Math worksheets and
visual curriculum