Sin 1: Overview, Questions, Preparation

The magnitude of sin 1 in radian is 0.8414709848. In trigonometry, the full trigonometric functions and calculations are based on three main ratios, i.e., sine, cosine, and tangent trigonometry. These trigonometric ratios allow one to locate angles and lengths of sides in a triangle. The simple angles usually used to solve trigonometric problems are 0, 30, 45, 60, 90 degrees. These angles are often represented in the shape of radians such as Δ/2, Δ/3, Δ/4, Δ/6, Δ, and so on. 

Let us figure out how to measure the value of sin 1. 

The value of sine 1 in radian is 0.8414709848.

We know, π/3 = 1.047198≈1

Sin (π/3) = √3/2 and sin π = 0

Now using these data, we can write;

sin1=sin[π/3−(π/3−1)]

⟹sin1=sin(π/3)cos(π/3-1)−cosπ/3sin(π/3−1)

The angle π/3−1=0.047198 is a very small angle.

We know that, for small angles θ,

Sinθ ≈ θ and cos⁡θ ≈ 1

hence,

Sin 1 ≈ (√3/2×1)−[1/2×(π/3−1)]

Therefore,

⟹sin1 ≈ 0.842427

The sine of an angle, say x, will take radian or degrees as its statement. The law is to calculate radian.

Now, π radian = 180 degree

so, 1 rad = 180/π degree

1 rad = 57.2957795131 degree

In terms of degree, we know,

sin 0° = 0, sin 90° = 1

In radians,

sin 0 = 0 and sin (π/2)=1

Now, π = 3.14159265359, π/2=1.5707963268

Thus,

sin (1.5707963268)= 1, when the angle is in radian

So,

sin (1) = 0.8414709848 [when angle is in radian]

sin (57.2957795131) = 0.8414709848 [when angle is in degree]

The inverse sin of 1, i.e., sin-1 (1), is a very special value of the inverse sine equation. Sin-1(x) is going to give us an angle whose sine is x. Therefore, sin-1 (1) is equivalent to the angle at which sine is 1.

This concept is taught under the chapter Trigonometric Functions. In this you will learn about Sin 1, its value, and how it's calculated. This topic holds a weightage of 12-14 marks in your final exam.

1. What is the sin inverse value? 

The inverse sin of 1, i.e., sin-1 (1), is a very special value of the inverse sine equation. Sin-1(x) is going to give us an angle whose sine is x.

2. What is the value of sin45? 

The decimal value of Sin 45 degree is 0.7071067812. Sine is thought to be one of the most significant features of trigonometry since it is used to calculate the undefined values of the angles and the length of the sides of the right-angle triangle.

3. Why is tan 90 not defined? 

At 90 degrees, we have to assume that the tangent is unknown, so when you split the leg opposite the neighbouring leg, you cannot divide the leg by zero. In the third quadrant, the stretched hypotenuse would now meet the tangent line above the x-axis and is now optimistic again.

Q: What's the opposite of sine being called?

Q: What's the value of sin?

Q: Can you divide the trig function?

Q: What is the value of sin 30?

Q: The sin value of 30 degrees is 0.5.