Sin 69 Degrees

The value of sin 69 degrees is 0.9335804. . .. Sin 69 degrees in radians is written as sin (69° × π/180°), i.e., sin (23π/60) or sin (1.204277. . .). In this article, we will discuss the methods to find the value of sin 69 degrees with examples.

• Sin 69°: 0.9335804. . .
• Sin (-69 degrees): -0.9335804. . .
• Sin 69° in radians: sin (23π/60) or sin (1.2042771 . . .)

What is the Value of Sin 69 Degrees?

The value of sin 69 degrees in decimal is 0.933580426. . .. Sin 69 degrees can also be expressed using the equivalent of the given angle (69 degrees) in radians (1.20427 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 69 degrees = 69° × (π/180°) rad = 23π/60 or 1.2042 . . .
∴ sin 69° = sin(1.2042) = 0.9335804. . .

Explanation:

For sin 69 degrees, the angle 69° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 69° value = 0.9335804. . .
Since the sine function is a periodic function, we can represent sin 69° as, sin 69 degrees = sin(69° + n × 360°), n ∈ Z.
⇒ sin 69° = sin 429° = sin 789°, and so on.
Note: Since, sine is an odd function, the value of sin(-69°) = -sin(69°).

Methods to Find Value of Sin 69 Degrees

The sine function is positive in the 1st quadrant. The value of sin 69° is given as 0.93358. . .. We can find the value of sin 69 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 69 Degrees Using Unit Circle

To find the value of sin 69 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 69° angle with the positive x-axis.
• The sin of 69 degrees equals the y-coordinate(0.9336) of the point of intersection (0.3584, 0.9336) of unit circle and r.

Hence the value of sin 69° = y = 0.9336 (approx)

Sin 69° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 69 degrees as:

• ± √(1-cos²(69°))
• ± tan 69°/√(1 + tan²(69°))
• ± 1/√(1 + cot²(69°))
• ± √(sec²(69°) - 1)/sec 69°
• 1/cosec 69°

Note: Since 69° lies in the 1st Quadrant, the final value of sin 69° will be positive.

We can use trigonometric identities to represent sin 69° as,

• sin(180° - 69°) = sin 111°
• -sin(180° + 69°) = -sin 249°
• cos(90° - 69°) = cos 21°
• -cos(90° + 69°) = -cos 159°

☛ Also Check:

• sin 0 degrees
• sin 120 degrees
• sin 3 degrees
• sin 105 degrees
• sin 200 degrees
• sin 43 degrees

FAQs on Sin 69 Degrees

What is Sin 69 Degrees?

Sin 69 degrees is the value of sine trigonometric function for an angle equal to 69 degrees. The value of sin 69° is 0.9336 (approx).

How to Find the Value of Sin 69 Degrees?

The value of sin 69 degrees can be calculated by constructing an angle of 69° with the x-axis, and then finding the coordinates of the corresponding point (0.3584, 0.9336) on the unit circle. The value of sin 69° is equal to the y-coordinate (0.9336). ∴ sin 69° = 0.9336.

What is the Value of Sin 69 Degrees in Terms of Cot 69°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 69° can be written as 1/√(1 + cot²(69°)). Here, the value of cot 69° is equal to 0.38386.

How to Find Sin 69° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 69° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(69°))
• ± tan 69°/√(1 + tan²(69°))
• ± 1/√(1 + cot²(69°))
• ± √(sec²(69°) - 1)/sec 69°
• 1/cosec 69°

☛ Also check: trigonometry table

What is the Exact Value of sin 69 Degrees?

The exact value of sin 69 degrees can be given accurately up to 8 decimal places as 0.93358042.