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Cos 77 Degrees

The value of cos 77 degrees is 0.2249510. . .. Cos 77 degrees in radians is written as cos (77° × π/180°), i.e., cos (1.343903. . .). In this article, we will discuss the methods to find the value of cos 77 degrees with examples.

  • Cos 77°: 0.2249510. . .
  • Cos (-77 degrees): 0.2249510. . .
  • Cos 77° in radians: cos (1.3439035 . . .)

What is the Value of Cos 77 Degrees?

The value of cos 77 degrees in decimal is 0.224951054. . .. Cos 77 degrees can also be expressed using the equivalent of the given angle (77 degrees) in radians (1.34390 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 77 degrees = 77° × (π/180°) rad = 1.3439 . . .
∴ cos 77° = cos(1.3439) = 0.2249510. . .

Cos 77 Degrees

Explanation:

For cos 77 degrees, the angle 77° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 77° value = 0.2249510. . .
Since the cosine function is a periodic function, we can represent cos 77° as, cos 77 degrees = cos(77° + n × 360°), n ∈ Z.
⇒ cos 77° = cos 437° = cos 797°, and so on.
Note: Since, cosine is an even function, the value of cos(-77°) = cos(77°).

Methods to Find Value of Cos 77 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 77° is given as 0.22495. . .. We can find the value of cos 77 degrees by:

  • Using Trigonometric Functions
  • Using Unit Circle

Cos 77° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 77 degrees as:

  • ± √(1-sin²(77°))
  • ± 1/√(1 + tan²(77°))
  • ± cot 77°/√(1 + cot²(77°))
  • ±√(cosec²(77°) - 1)/cosec 77°
  • 1/sec 77°

Note: Since 77° lies in the 1st Quadrant, the final value of cos 77° will be positive.

We can use trigonometric identities to represent cos 77° as,

  • -cos(180° - 77°) = -cos 103°
  • -cos(180° + 77°) = -cos 257°
  • sin(90° + 77°) = sin 167°
  • sin(90° - 77°) = sin 13°

Cos 77 Degrees Using Unit Circle

value of cos 77

To find the value of cos 77 degrees using the unit circle:

  • Rotate ‘r’ anticlockwise to form 77° angle with the positive x-axis.
  • The cos of 77 degrees equals the x-coordinate(0.225) of the point of intersection (0.225, 0.9744) of unit circle and r.

Hence the value of cos 77° = x = 0.225 (approx)

☛ Also Check:

Examples Using Cos 77 Degrees

  1. Example 1: Simplify: 4 (cos 77°/sin 167°)

    Solution:

    We know cos 77° = sin 167°
    ⇒ 4 cos 77°/sin 167° = 4 (cos 77°/cos 77°)
    = 4(1) = 4

  2. Example 2: Find the value of (cos² 38.5° - sin² 38.5°). [Hint: Use cos 77° = 0.225]

    Solution:

    Using the cos 2a formula,
    (cos² 38.5° - sin² 38.5°) = cos(2 × 38.5°) = cos 77°
    ∵ cos 77° = 0.225
    ⇒ (cos² 38.5° - sin² 38.5°) = 0.225

  3. Example 3: Find the value of 2 cos(77°)/3 sin(13°).

    Solution:

    Using trigonometric identities, we know, cos(77°) = sin(90° - 77°) = sin 13°.
    ⇒ cos(77°) = sin(13°)
    ⇒ Value of 2 cos(77°)/3 sin(13°) = 2/3

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FAQs on Cos 77 Degrees

What is Cos 77 Degrees?

Cos 77 degrees is the value of cosine trigonometric function for an angle equal to 77 degrees. The value of cos 77° is 0.225 (approx)

What is the Value of Cos 77 Degrees in Terms of Tan 77°?

We know, using trig identities, we can write cos 77° as 1/√(1 + tan²(77°)). Here, the value of tan 77° is equal to 4.331475.

How to Find Cos 77° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 77° can be given in terms of other trigonometric functions as:

  • ± √(1-sin²(77°))
  • ± 1/√(1 + tan²(77°))
  • ± cot 77°/√(1 + cot²(77°))
  • ± √(cosec²(77°) - 1)/cosec 77°
  • 1/sec 77°

☛ Also check: trigonometric table

How to Find the Value of Cos 77 Degrees?

The value of cos 77 degrees can be calculated by constructing an angle of 77° with the x-axis, and then finding the coordinates of the corresponding point (0.225, 0.9744) on the unit circle. The value of cos 77° is equal to the x-coordinate (0.225). ∴ cos 77° = 0.225.

What is the Exact Value of cos 77 Degrees?

The exact value of cos 77 degrees can be given accurately up to 8 decimal places as 0.22495105.

 
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