Sin 70 Degrees

The value of sin 70 degrees is 0.9396926. . .. Sin 70 degrees in radians is written as sin (70° × π/180°), i.e., sin (7π/18) or sin (1.221730. . .). In this article, we will discuss the methods to find the value of sin 70 degrees with examples.

• Sin 70°: 0.9396926. . .
• Sin (-70 degrees): -0.9396926. . .
• Sin 70° in radians: sin (7π/18) or sin (1.2217304 . . .)

What is the Value of Sin 70 Degrees?

The value of sin 70 degrees in decimal is 0.939692620. . .. Sin 70 degrees can also be expressed using the equivalent of the given angle (70 degrees) in radians (1.22173 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 70 degrees = 70° × (π/180°) rad = 7π/18 or 1.2217 . . .
∴ sin 70° = sin(1.2217) = 0.9396926. . .

Explanation:

For sin 70 degrees, the angle 70° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 70° value = 0.9396926. . .
Since the sine function is a periodic function, we can represent sin 70° as, sin 70 degrees = sin(70° + n × 360°), n ∈ Z.
⇒ sin 70° = sin 430° = sin 790°, and so on.
Note: Since, sine is an odd function, the value of sin(-70°) = -sin(70°).

Methods to Find Value of Sin 70 Degrees

The sine function is positive in the 1st quadrant. The value of sin 70° is given as 0.93969. . .. We can find the value of sin 70 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 70° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 70 degrees as:

• ± √(1-cos²(70°))
• ± tan 70°/√(1 + tan²(70°))
• ± 1/√(1 + cot²(70°))
• ± √(sec²(70°) - 1)/sec 70°
• 1/cosec 70°

Note: Since 70° lies in the 1st Quadrant, the final value of sin 70° will be positive.

We can use trigonometric identities to represent sin 70° as,

• sin(180° - 70°) = sin 110°
• -sin(180° + 70°) = -sin 250°
• cos(90° - 70°) = cos 20°
• -cos(90° + 70°) = -cos 160°

Sin 70 Degrees Using Unit Circle

To find the value of sin 70 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 70° angle with the positive x-axis.
• The sin of 70 degrees equals the y-coordinate(0.9397) of the point of intersection (0.342, 0.9397) of unit circle and r.

Hence the value of sin 70° = y = 0.9397 (approx)

☛ Also Check:

• sin 36 degrees
• sin 11 degrees
• sin 45 degrees
• sin 129 degrees
• sin 600 degrees
• sin 1500 degrees

FAQs on Sin 70 Degrees

What is Sin 70 Degrees?

Sin 70 degrees is the value of sine trigonometric function for an angle equal to 70 degrees. The value of sin 70° is 0.9397 (approx).

How to Find Sin 70° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 70° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(70°))
• ± tan 70°/√(1 + tan²(70°))
• ± 1/√(1 + cot²(70°))
• ± √(sec²(70°) - 1)/sec 70°
• 1/cosec 70°

☛ Also check: trigonometric table

What is the Value of Sin 70 Degrees in Terms of Cos 70°?

Using trigonometric identities, we can write sin 70° in terms of cos 70° as, sin(70°) = √(1-cos²(70°)). Here, the value of cos 70° is equal to 0.3420201.

What is the Exact Value of sin 70 Degrees?

The exact value of sin 70 degrees can be given accurately up to 8 decimal places as 0.93969262.

How to Find the Value of Sin 70 Degrees?

The value of sin 70 degrees can be calculated by constructing an angle of 70° with the x-axis, and then finding the coordinates of the corresponding point (0.342, 0.9397) on the unit circle. The value of sin 70° is equal to the y-coordinate (0.9397). ∴ sin 70° = 0.9397.