Cos 33 Degrees

The value of cos 33 degrees is 0.8386705. . .. Cos 33 degrees in radians is written as cos (33° × π/180°), i.e., cos (11π/60) or cos (0.575958. . .). In this article, we will discuss the methods to find the value of cos 33 degrees with examples.

• Cos 33°: 0.8386705. . .
• Cos (-33 degrees): 0.8386705. . .
• Cos 33° in radians: cos (11π/60) or cos (0.5759586 . . .)

What is the Value of Cos 33 Degrees?

The value of cos 33 degrees in decimal is 0.838670567. . .. Cos 33 degrees can also be expressed using the equivalent of the given angle (33 degrees) in radians (0.57595 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 33 degrees = 33° × (π/180°) rad = 11π/60 or 0.5759 . . .
∴ cos 33° = cos(0.5759) = 0.8386705. . .

Explanation:

For cos 33 degrees, the angle 33° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 33° value = 0.8386705. . .
Since the cosine function is a periodic function, we can represent cos 33° as, cos 33 degrees = cos(33° + n × 360°), n ∈ Z.
⇒ cos 33° = cos 393° = cos 753°, and so on.
Note: Since, cosine is an even function, the value of cos(-33°) = cos(33°).

Methods to Find Value of Cos 33 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 33° is given as 0.83867. . .. We can find the value of cos 33 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 33° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 33 degrees as:

• ± √(1-sin²(33°))
• ± 1/√(1 + tan²(33°))
• ± cot 33°/√(1 + cot²(33°))
• ±√(cosec²(33°) - 1)/cosec 33°
• 1/sec 33°

Note: Since 33° lies in the 1st Quadrant, the final value of cos 33° will be positive.

We can use trigonometric identities to represent cos 33° as,

• -cos(180° - 33°) = -cos 147°
• -cos(180° + 33°) = -cos 213°
• sin(90° + 33°) = sin 123°
• sin(90° - 33°) = sin 57°

Cos 33 Degrees Using Unit Circle

To find the value of cos 33 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 33° angle with the positive x-axis.
• The cos of 33 degrees equals the x-coordinate(0.8387) of the point of intersection (0.8387, 0.5446) of unit circle and r.

Hence the value of cos 33° = x = 0.8387 (approx)

☛ Also Check:

• cos 40 degrees
• cos 37 degrees
• cos 300 degrees
• cos 1140 degrees
• cos 68 degrees
• cos 59 degrees

FAQs on Cos 33 Degrees

What is Cos 33 Degrees?

Cos 33 degrees is the value of cosine trigonometric function for an angle equal to 33 degrees. The value of cos 33° is 0.8387 (approx)

How to Find the Value of Cos 33 Degrees?

The value of cos 33 degrees can be calculated by constructing an angle of 33° with the x-axis, and then finding the coordinates of the corresponding point (0.8387, 0.5446) on the unit circle. The value of cos 33° is equal to the x-coordinate (0.8387). ∴ cos 33° = 0.8387.

How to Find Cos 33° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 33° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(33°))
• ± 1/√(1 + tan²(33°))
• ± cot 33°/√(1 + cot²(33°))
• ± √(cosec²(33°) - 1)/cosec 33°
• 1/sec 33°

☛ Also check: trigonometry table

What is the Exact Value of cos 33 Degrees?

The exact value of cos 33 degrees can be given accurately up to 8 decimal places as 0.83867056.

What is the Value of Cos 33 Degrees in Terms of Tan 33°?

We know, using trig identities, we can write cos 33° as 1/√(1 + tan²(33°)). Here, the value of tan 33° is equal to 0.649407.