Cos 70 Degrees

The value of cos 70 degrees is 0.3420201. . .. Cos 70 degrees in radians is written as cos (70° × π/180°), i.e., cos (7π/18) or cos (1.221730. . .). In this article, we will discuss the methods to find the value of cos 70 degrees with examples.

• Cos 70°: 0.3420201. . .
• Cos (-70 degrees): 0.3420201. . .
• Cos 70° in radians: cos (7π/18) or cos (1.2217304 . . .)

What is the Value of Cos 70 Degrees?

The value of cos 70 degrees in decimal is 0.342020143. . .. Cos 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 . . .
∴ cos 70° = cos(1.2217) = 0.3420201. . .

Explanation:

For cos 70 degrees, the angle 70° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 70° value = 0.3420201. . .
Since the cosine function is a periodic function, we can represent cos 70° as, cos 70 degrees = cos(70° + n × 360°), n ∈ Z.
⇒ cos 70° = cos 430° = cos 790°, and so on.
Note: Since, cosine is an even function, the value of cos(-70°) = cos(70°).

Methods to Find Value of Cos 70 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 70° is given as 0.34202. . .. We can find the value of cos 70 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 70° in Terms of Trigonometric Functions

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

• ± √(1-sin²(70°))
• ± 1/√(1 + tan²(70°))
• ± cot 70°/√(1 + cot²(70°))
• ±√(cosec²(70°) - 1)/cosec 70°
• 1/sec 70°

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

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

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

Cos 70 Degrees Using Unit Circle

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

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

Hence the value of cos 70° = x = 0.342 (approx)

☛ Also Check:

• cos 18 degrees
• cos 40 degrees
• cos 11 degrees
• cos 79 degrees
• cos 58 degrees
• cos 85 degrees

FAQs on Cos 70 Degrees

What is Cos 70 Degrees?

Cos 70 degrees is the value of cosine trigonometric function for an angle equal to 70 degrees. The value of cos 70° is 0.342 (approx)

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

Using trigonometric identities, we can write cos 70° in terms of sin 70° as, cos(70°) = √(1 - sin²(70°)). Here, the value of sin 70° is equal to 0.9397.

What is the Value of Cos 70° in Terms of Cosec 70°?

Since the cosine function can be represented using the cosecant function, we can write cos 70° as [√(cosec²(70°) - 1)/cosec 70°]. The value of cosec 70° is equal to 1.06417.

How to Find the Value of Cos 70 Degrees?

The value of cos 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 cos 70° is equal to the x-coordinate (0.342). ∴ cos 70° = 0.342.

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

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

• ± √(1-sin²(70°))
• ± 1/√(1 + tan²(70°))
• ± cot 70°/√(1 + cot²(70°))
• ± √(cosec²(70°) - 1)/cosec 70°
• 1/sec 70°

☛ Also check: trigonometric table