# Tan 105 Tan 15

Tan 105 Tan 15.

## Tan 165 Degrees

The value of
tan 165 degrees is -0.2679491. . .. Tan 165 degrees in radians is written as tan (165° × π/180°), i.e., tan (11π/12) or tan (2.879793. . .). In this article, we will discuss the methods to find the value of tan 165 degrees with examples.

• Tan 165°:
-2 + √3
• Tan 165° in decimal:
-0.2679491. . .
• Tan (-165 degrees):
0.2679491. . . or 2 – √3

tan (11π/12) or tan (two.8797932 . . .)

## What is the Value of Tan 165 Degrees?

The value of tan 165 degrees in decimal is -0.267949192. . .. Tan 165 degrees can as well be expressed using the equivalent of the given angle (165 degrees) in radians (2.87979 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 165 degrees = 165° × (π/180°) rad = 11π/12 or 2.8797 . . .
∴ tan 165° = tan(2.8797) = -2 + √three or -0.2679491. . . Explanation:

For tan 165 degrees, the angle 165° lies between 90° and 180° (2nd Quadrant). Since tangent function is negative in the 2d quadrant, thus tan 165° value = -2 + √3 or -0.2679491. . .
Since the tangent office is a periodic function, nosotros can stand for tan 165° as, tan 165 degrees = tan(165° + n × 180°), n ∈ Z.
⇒ tan 165° = tan 345° = tan 525°, and so on.
Note:
Since, tangent is an odd function, the value of tan(-165°) = -tan(165°).

Baca :   Contoh Soal Tentang Hukum Archimedes

## Methods to Find Value of Tan 165 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 165° is given equally -0.26794. . .. We can notice the value of tan 165 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

## Tan 165 Degrees Using Unit of measurement Circle To notice the value of tan 165 degrees using the unit of measurement circle:

• Rotate ‘r’ anticlockwise to form 165° bending with the positive ten-axis.
• The tan of 165 degrees equals the y-coordinate(0.2588) divided by x-coordinate(-0.9659) of the point of intersection (-0.9659, 0.2588) of unit circumvolve and r.

Hence the value of tan 165° = y/ten = -0.2679 (approx).

## Tan 165° in Terms of Trigonometric Functions

Using trigonometry formulas, we tin represent the tan 165 degrees equally:

• sin(165°)/cos(165°)
• ± sin 165°/√(1 – sin²(165°))
• ± √(1 – cos²(165°))/cos 165°
• ± one/√(cosec²(165°) – 1)
• ± √(sec²(165°) – one)
• ane/cot 165°

Note: Since 165° lies in the 2nd Quadrant, the concluding value of tan 165° will be negative.

We tin use trigonometric identities to represent tan 165° as,

• cot(90° – 165°) = cot(-75°)
• -cot(ninety° + 165°) = -cot 255°
• -tan (180° – 165°) = -tan xv°

☛ Also Check:

• tan 37 degrees
• tan ninety degrees
• tan 53 degrees
• tan 18 degrees
• tan 67 degrees
• tan 285 degrees

## FAQs on Tan 165 Degrees

### What is Tan 165 Degrees?

Tan 165 degrees is the value of tangent trigonometric function for an angle equal to 165 degrees.

The value of tan 165° is -2 + √3 or -0.2679 (approx).

### What is the Exact Value of tan 165 Degrees?

The
verbal value of tan 165 degrees
tin can be given accurately up to 8 decimal places as -0.26794919 or every bit -2 + √3.

Baca :   5 8 Diubah Menjadi Pecahan Desimal

### How to Observe Tan 165° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 165° tin exist given in terms of other trigonometric functions as:

• sin(165°)/cos(165°)
• ± sin 165°/√(1 – sin²(165°))
• ± √(one – cos²(165°))/cos 165°
• ± 1/√(cosec²(165°) – one)
• ± √(sec²(165°) – one)
• 1/cot 165°

☛ Also check: trigonometric table

### What is the Value of Tan 165 Degrees in Terms of Cot 165°?

Since the tangent function is the reciprocal of the cotangent part, we can write tan 165° equally 1/cot(165°). The value of cot 165° is equal to -(2 + √three).

### How to Notice the Value of Tan 165 Degrees?

The value of tan 165 degrees can exist calculated by constructing an angle of 165° with the x-axis, and and so finding the coordinates of the corresponding indicate (-0.9659, 0.2588) on the unit circle. The value of tan 165° is equal to the y-coordinate(0.2588) divided by the x-coordinate (-0.9659). ∴ tan 165° = -ii + √3 or -0.2679

## Tan 105 Tan 15

Source: https://www.cuemath.com/trigonometry/tan-165-degrees/

## Contoh Soal Perkalian Vektor

Contoh Soal Perkalian Vektor. Web log Koma – Setelah mempelajari beberapa operasi hitung pada vektor …