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

Cos 25 Degrees

The value of cos 25 degrees is 0.9063077. . .. Cos 25 degrees in radians is written as cos (25° × π/180°), i.e., cos (5π/36) or cos (0.436332. . .). In this article, we will discuss the methods to find the value of cos 25 degrees with examples.

  • Cos 25°: 0.9063077. . .
  • Cos (-25 degrees): 0.9063077. . .
  • Cos 25° in radians: cos (5π/36) or cos (0.4363323 . . .)

What is the Value of Cos 25 Degrees?

The value of cos 25 degrees in decimal is 0.906307787. . .. Cos 25 degrees can also be expressed using the equivalent of the given angle (25 degrees) in radians (0.43633 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 25 degrees = 25° × (π/180°) rad = 5π/36 or 0.4363 . . .
∴ cos 25° = cos(0.4363) = 0.9063077. . .

Cos 25 Degrees

Explanation:

For cos 25 degrees, the angle 25° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 25° value = 0.9063077. . .
Since the cosine function is a periodic function, we can represent cos 25° as, cos 25 degrees = cos(25° + n × 360°), n ∈ Z.
⇒ cos 25° = cos 385° = cos 745°, and so on.
Note: Since, cosine is an even function, the value of cos(-25°) = cos(25°).

Methods to Find Value of Cos 25 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 25° is given as 0.90630. . .. We can find the value of cos 25 degrees by:

  • Using Unit Circle
  • Using Trigonometric Functions

Cos 25 Degrees Using Unit Circle

value of cos 25

To find the value of cos 25 degrees using the unit circle:

  • Rotate ‘r’ anticlockwise to form 25° angle with the positive x-axis.
  • The cos of 25 degrees equals the x-coordinate(0.9063) of the point of intersection (0.9063, 0.4226) of unit circle and r.

Hence the value of cos 25° = x = 0.9063 (approx)

Cos 25° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 25 degrees as:

  • ± √(1-sin²(25°))
  • ± 1/√(1 + tan²(25°))
  • ± cot 25°/√(1 + cot²(25°))
  • ±√(cosec²(25°) - 1)/cosec 25°
  • 1/sec 25°

Note: Since 25° lies in the 1st Quadrant, the final value of cos 25° will be positive.

We can use trigonometric identities to represent cos 25° as,

  • -cos(180° - 25°) = -cos 155°
  • -cos(180° + 25°) = -cos 205°
  • sin(90° + 25°) = sin 115°
  • sin(90° - 25°) = sin 65°

☛ Also Check:

Examples Using Cos 25 Degrees

  1. Example 1: Find the value of (cos² 12.5° - sin² 12.5°). [Hint: Use cos 25° = 0.9063]

    Solution:

    Using the cos 2a formula,
    (cos² 12.5° - sin² 12.5°) = cos(2 × 12.5°) = cos 25°
    ∵ cos 25° = 0.9063
    ⇒ (cos² 12.5° - sin² 12.5°) = 0.9063

  2. Example 2: Find the value of 2 cos(25°)/3 sin(65°).

    Solution:

    Using trigonometric identities, we know, cos(25°) = sin(90° - 25°) = sin 65°.
    ⇒ cos(25°) = sin(65°)
    ⇒ Value of 2 cos(25°)/3 sin(65°) = 2/3

  3. Example 3: Simplify: 5 (cos 25°/sin 115°)

    Solution:

    We know cos 25° = sin 115°
    ⇒ 5 cos 25°/sin 115° = 5 (cos 25°/cos 25°)
    = 5(1) = 5

Show Solution >

go to slidego to slidego 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 Cos 25 Degrees

What is Cos 25 Degrees?

Cos 25 degrees is the value of cosine trigonometric function for an angle equal to 25 degrees. The value of cos 25° is 0.9063 (approx)

How to Find Cos 25° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 25° can be given in terms of other trigonometric functions as:

  • ± √(1-sin²(25°))
  • ± 1/√(1 + tan²(25°))
  • ± cot 25°/√(1 + cot²(25°))
  • ± √(cosec²(25°) - 1)/cosec 25°
  • 1/sec 25°

☛ Also check: trigonometric table

How to Find the Value of Cos 25 Degrees?

The value of cos 25 degrees can be calculated by constructing an angle of 25° with the x-axis, and then finding the coordinates of the corresponding point (0.9063, 0.4226) on the unit circle. The value of cos 25° is equal to the x-coordinate (0.9063). ∴ cos 25° = 0.9063.

What is the Value of Cos 25 Degrees in Terms of Tan 25°?

We know, using trig identities, we can write cos 25° as 1/√(1 + tan²(25°)). Here, the value of tan 25° is equal to 0.466307.

What is the Value of Cos 25° in Terms of Sec 25°?

Since the secant function is the reciprocal of the cosine function, we can write cos 25° as 1/sec(25°). The value of sec 25° is equal to 1.103377.

 
Download FREE Study Materials
Trigonometry
Math worksheets and
visual curriculum