Sin Cos Tan Table – Formulas, Values, Examples, and FAQ

Sin Cos Tan Table 

The trigonometric functions sin, cos and tan are the primary functions we consider while solving trigonometric questions. ‘Sin cos tan table’ consists of sin, cos and tan values of standard angles 0°, 30°, 45°, 60° and 90°, sometimes other angles like 180°, 270°, and 360° also.

Sin Cos Tan Formula

The three ratios sin, cos, and tan have their individual formulas. Suppose ABC is a right-angled triangle, right-angled at B, as shown in the figure below:

The three sides in the right-angled triangle are given below:

AB = Adjacent side to angle θ

BC = Opposite side to angle θ

CA = Hypotenuse to angle θ

Now as per sin, cos and tan formulas, we have:

sin θ = Opposite side / Hypotenuse = BC / CA

cos θ = Adjacent side / Hypotenuse = AB / CA

tan θ = Opposite side / Adjacent side = CB / AB

Sin Cos Tan Chart (Table)

Let us see the table where the values of sin, cos, and tan are provided for the standard angles 0°, 30° (π/6), 45° (π/4), 60° (π/3) and 90° (π/2).

How to Remember Sin Cos Tan Values?

For finding sin, cos, tan values, follow the below steps:

• Create a table and list the first row with angles 0°, 30°, 45°, 60°, 90°, and write the trigonometric function name in the first column, such as sin.

• Now we will determine the values for sin. Write numbers 0, 1, 2, 3, 4 under the angles 0°, 30°, 45°, 60°, 90° respectively. 

• Now divide the numbers by 4 and find the square root. We will get √(0/4), √(¼), √(2/4), √(¾), and √(4/4). 

• On simplifying this, we will get the values of sine for these 5 angles. 

• Now for the remaining three angles, use the following formulas:

sin (180° − x) = sin x

sin (180° + x) = – (sin x)

sin (360° − x) = – (sin x)

This means,

sin 180° = sin (180° − 0°) = sin 0° = 0

sin 270° = sin (180° +90°) = – (sin 90°) = -1

Sin 360° = sin (360° − 0°) = – (sin 0°) = 0

• Now we will determine the values for cos using the formula cos x = sin (90° – x). For example, cos 60° = sin (90° – 30°) = sin 30° = ½. Similarly, you can find out the other values.

• To determine the values for tan, we use the formula tan x = (sin x/cos x).

For example, the value of tan 30° = (sin 30°/cos 30°) = (½) /(√3/2) = (1/√3). Similarly, we can generate the other values. 

The value of trigonometric functions for angles ranging from 0º to 360º is given in the following trigonometry table. 

Examples

1. What is the value of sin 270°?

We know that, sin 270° = sin (180° + 90°) 

Also, sin (180° + x) = – (sin x)

Therefore, sin (180° + 90°) = – sin 90° = – 1

Hence, sin 270° = – 1

2. Use the trigonometry table and write the values of:

(a) sin(π/4) (b) cos(π/3) (c) tan (π/2)

The trigonometry table helps us to find these values quickly. We have:

(a) sin(π/4) = sin 45º = (1/√2)

(b) cos(π/3) = cos 60º = (1/2)

(c) tan (π/2) = tan 90º = ∞