Sin 67 Degrees

The value of sin 67 degrees is 0.9205048. . .. Sin 67 degrees in radians is written as sin (67° × π/180°), i.e., sin (1.169370. . .). In this article, we will discuss the methods to find the value of sin 67 degrees with examples.

• Sin 67°: 0.9205048. . .
• Sin (-67 degrees): -0.9205048. . .
• Sin 67° in radians: sin (1.1693705 . . .)

What is the Value of Sin 67 Degrees?

The value of sin 67 degrees in decimal is 0.920504853. . .. Sin 67 degrees can also be expressed using the equivalent of the given angle (67 degrees) in radians (1.16937 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 67 degrees = 67° × (π/180°) rad = 1.1693 . . .
∴ sin 67° = sin(1.1693) = 0.9205048. . .

Explanation:

For sin 67 degrees, the angle 67° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 67° value = 0.9205048. . .
Since the sine function is a periodic function, we can represent sin 67° as, sin 67 degrees = sin(67° + n × 360°), n ∈ Z.
⇒ sin 67° = sin 427° = sin 787°, and so on.
Note: Since, sine is an odd function, the value of sin(-67°) = -sin(67°).

Methods to Find Value of Sin 67 Degrees

The sine function is positive in the 1st quadrant. The value of sin 67° is given as 0.92050. . .. We can find the value of sin 67 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 67° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 67 degrees as:

• ± √(1-cos²(67°))
• ± tan 67°/√(1 + tan²(67°))
• ± 1/√(1 + cot²(67°))
• ± √(sec²(67°) - 1)/sec 67°
• 1/cosec 67°

Note: Since 67° lies in the 1st Quadrant, the final value of sin 67° will be positive.

We can use trigonometric identities to represent sin 67° as,

• sin(180° - 67°) = sin 113°
• -sin(180° + 67°) = -sin 247°
• cos(90° - 67°) = cos 23°
• -cos(90° + 67°) = -cos 157°

Sin 67 Degrees Using Unit Circle

To find the value of sin 67 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 67° angle with the positive x-axis.
• The sin of 67 degrees equals the y-coordinate(0.9205) of the point of intersection (0.3907, 0.9205) of unit circle and r.

Hence the value of sin 67° = y = 0.9205 (approx)

☛ Also Check:

• sin 360 degrees
• sin 20 degrees
• sin 10 degrees
• sin 1000 degrees
• sin 42 degrees
• sin 330 degrees

FAQs on Sin 67 Degrees

What is Sin 67 Degrees?

Sin 67 degrees is the value of sine trigonometric function for an angle equal to 67 degrees. The value of sin 67° is 0.9205 (approx).

What is the Value of Sin 67° in Terms of Sec 67°?

Since the sine function can be represented using the secant function, we can write sin 67° as √(sec²(67°) - 1)/sec 67°. The value of sec 67° is equal to 2.559305.

How to Find the Value of Sin 67 Degrees?

The value of sin 67 degrees can be calculated by constructing an angle of 67° with the x-axis, and then finding the coordinates of the corresponding point (0.3907, 0.9205) on the unit circle. The value of sin 67° is equal to the y-coordinate (0.9205). ∴ sin 67° = 0.9205.

How to Find Sin 67° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 67° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(67°))
• ± tan 67°/√(1 + tan²(67°))
• ± 1/√(1 + cot²(67°))
• ± √(sec²(67°) - 1)/sec 67°
• 1/cosec 67°

☛ Also check: trigonometry table

What is the Value of Sin 67 Degrees in Terms of Cos 67°?

Using trigonometric identities, we can write sin 67° in terms of cos 67° as, sin(67°) = √(1-cos²(67°)). Here, the value of cos 67° is equal to 0.3907311.