Question

hey

find the value of Tan855° ?

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Answer 1

here is ur answer hope it helped u

Answer 2

$\huge\mathfrak\blue{ANSWER .... }$

The value of tan 855 degrees is -1. Tan 855 degrees can also be expressed using the equivalent of the given angle (855 degrees) in radians (14.92256 . . .

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)

$⇒ 855 \: degrees = 855° × (π/180°) rad = 19π/4 \: or 14.9225 . . .$

$∴ tan \: 855° = tan \: (14.9225) = -1$

Explanation:-

For tan 855°, the angle 855° > 360°.

We can represent tan 855° as, tan(855° mod 360°) = tan(135°). The angle 855°, coterminal to angle 135°, is located in the Second Quadrant(Quadrant II).

Since tangent function is negative in the 2nd quadrant, thus tan 855 degrees value = -1

Similarly, given the periodic property of tan 855°, it can also be written as, tan 855 degrees =

$= (855° + n × 180°), n ∈ Z.</p><p>⇒ tan \: 855° = tan \: 1035° = tan \: 1215°, and \: so \: on.$

$\small\mathfrak\green{important \: note}$

Since, tangent is an odd function, the value of tan(-855°) = -tan(855°).

Methods to Find Value of Tan 855 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 855° is given as -1. We can find the value of tan 855 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 855 Degrees Using Unit Circle

To find the value of tan 855 degrees using the unit circle, represent 855° in the form (2 × 360°) + 135° [∵ 855°>360°] ∵ The angle 855° is coterminal to 135° angle and also tangent is a periodic function, tan 855° = tan 135°.

$sin(855°)/cos(855°) \\ ± sin 855°/√(1 - sin²(855)) \\ ± √(1 - cos²(855°)) \\ /cos 855°± 1/√(cosec²(855°) - 1) \\ ± √(sec²(855°) - 1)1/cot 855°$

Since 855° lies in the 2nd Quadrant, the final value of tan 855° will be negative.

We can use trigonometric identities to represent tan 855° as,

$cot(90° - 855°) = cot(-765°) \\ -cot(90° + 855°) \\ = -cot 945°-tan (180° - 855°) = -tan(-675°)$

$\huge\mathfrak\green{hence \: proved}$