Как найти sin 510

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The value of sin 510 degrees is 0.5. Sin 510 degrees in radians is written as sin (510° × π/180°), i.e., sin (17π/6) or sin (8.901179. . .). In this article, we will discuss the methods to find the value of sin 510 degrees with examples.

• Sin 510°: 0.5
• Sin 510° in fraction: 1/2
• Sin (-510 degrees): -0.5
• Sin 510° in radians: sin (17π/6) or sin (8.9011791 . . .)

What is the Value of Sin 510 Degrees?

The value of sin 510 degrees in decimal is 0.5. Sin 510 degrees can also be expressed using the equivalent of the given angle (510 degrees) in radians (8.90117 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 510 degrees = 510° × (π/180°) rad = 17π/6 or 8.9011 . . .
∴ sin 510° = sin(8.9011) = 1/2 or 0.5

Explanation:

For sin 510°, the angle 510° > 360°. Given the periodic property of the sine function, we can represent it as sin(510° mod 360°) = sin(150°). The angle 510°, coterminal to angle 150°, is located in the Second Quadrant(Quadrant II).
Since sine function is positive in the 2nd quadrant, thus sin 510 degrees value = 1/2 or 0.5
Similarly, sin 510° can also be written as, sin 510 degrees = (510° + n × 360°), n ∈ Z.
⇒ sin 510° = sin 870° = sin 1230°, and so on.
Note: Since, sine is an odd function, the value of sin(-510°) = -sin(510°).

Methods to Find Value of Sin 510 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 510° is given as 0.5. We can find the value of sin 510 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 510 Degrees Using Unit Circle

To find the value of sin 510 degrees using the unit circle, represent 510° in the form (1 × 360°) + 150° [∵ 510°>360°] ∵ sine is a periodic function, sin 510° = sin 150°.

• Rotate ‘r’ anticlockwise to form a 150° or 510° angle with the positive x-axis.
• The sin of 510 degrees equals the y-coordinate(0.5) of the point of intersection (-0.866, 0.5) of unit circle and r.

Hence the value of sin 510° = y = 0.5

Sin 510° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 510 degrees as:

• ± √(1-cos²(510°))
• ± tan 510°/√(1 + tan²(510°))
• ± 1/√(1 + cot²(510°))
• ± √(sec²(510°) — 1)/sec 510°
• 1/cosec 510°

Note: Since 510° lies in the 2nd Quadrant, the final value of sin 510° will be positive.

We can use trigonometric identities to represent sin 510° as,

• sin(180° — 510°) = sin(-330°)
• -sin(180° + 510°) = -sin 690°
• cos(90° — 510°) = cos(-420°)
• -cos(90° + 510°) = -cos 600°

☛ Also Check:

• sin 104 degrees
• sin 60 degrees
• sin 10 degrees
• sin 67 degrees
• sin 230 degrees
• sin 21 degrees

FAQs on Sin 510 Degrees

What is Sin 510 Degrees?

Sin 510 degrees is the value of sine trigonometric function for an angle equal to 510 degrees. The value of sin 510° is 1/2 or 0.5.

How to Find the Value of Sin 510 Degrees?

The value of sin 510 degrees can be calculated by constructing an angle of 510° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, 0.5) on the unit circle. The value of sin 510° is equal to the y-coordinate (0.5). ∴ sin 510° = 0.5.

How to Find Sin 510° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 510° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(510°))
• ± tan 510°/√(1 + tan²(510°))
• ± 1/√(1 + cot²(510°))
• ± √(sec²(510°) — 1)/sec 510°
• 1/cosec 510°

☛ Also check: trigonometric table

What is the Value of Sin 510 Degrees in Terms of Tan 510°?

We know, using trig identities, we can write sin 510° as -tan 510°/√(1 + tan²(510°)). Here, the value of tan 510° is equal to -0.577350.

What is the Exact Value of sin 510 Degrees?

The exact value of sin 510 degrees is 0.5.

Ответ:

sin510 = 1/2, cos510 =- 3/2, tg510 = — 3/3

Пошаговое изъяснение:

Первым делом всегда выделяйте полный угол, т.е. 360. Выделили — отбрасывайте, он нам не нужен. Отбрасывать можно поэтому, что функция синуса повторяющаяся, с периодом в один полный угол. Остаётся 510 — 360 = 150.

Вторым делом приводите этот угол с подмогою формул приведения к табличным значениям: 150 = 180 — 30. Потому

sin(180 — 30) = sin30 = 1/2.

Как следует, и sin510 = 1/2.

Соответственно, cos(180 — 30) = — cos30 = — 3/2.

Тангенс tg510 = sin510/cos510 = 1/2 : — 3/2 = — 3/3