In trigonometry, sin cos và tan values are the primary functions we consider while solving trigonometric problems. These trigonometry values are used to lớn measure the angles & sides of a right-angle triangle. Apart from sine, cosine & tangent values, the other three major values are cotangent, secant and cosecant.

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When we find sin cos và tan values for a triangle, we usually consider these angles: 0°, 30°, 45°, 60° và 90°. It is easy khổng lồ memorise the values for these certain angles. The trigonometric values are about the knowledge of standard angles for a given triangle as per the trigonometric ratios (sine, cosine, tangent, cotangent, secant & cosecant).

Sin Cos tan Formula

The three ratios, i.e. Sine, cosine and tangent have their individual formulas. Suppose, ABC is a right triangle, right-angled at B, as shown in the figure below:

*

Now as per sine, cosine & tangent formulas, we have here:

Sine θ = Opposite side/Hypotenuse = BC/ACCos θ = Adjacent side/Hypotenuse = AB/ACTan θ = Opposite side/Adjacent side = BC/AB

We can see clearly from the above formulas, that:

Tan θ = sin θ/cos θ

Now, the formulas for other trigonometry ratios are:

Cot θ = 1/tan θ = Adjacent side/ Side opposite = AB/BCSec θ = 1/Cos θ = Hypotenuse / Adjacent side = AC / ABCosec θ = 1/Sin θ = Hypotenuse / Side opposite = AC / BC

The other side of representation of trigonometric values formulas are:

Tan θ = sin θ/cos θCot θ = cos θ/sin θSin θ = rã θ/sec θCos θ = sin θ/tan θSec θ = rã θ/sin θCosec θ = sec θ/tan θ

Also, read:

Sin Cos tung Chart

Let us see the table where the values of sin cos tung sec cosec and tan are provided for the important angles 0°, 30°, 45°, 60° & 90°


Angles (in degrees)30°45°60°90°
Angles (in radian)0π/6π/4π/3π/2
Sin θ01/21/√2√3/21
Cos θ1√3/21/√21/20
Tan θ01/√31√3
Cot θ√311/√30
Sec θ12/√3√22
Cosec θ2√22/√31

How to find Sin Cos tung Values?

To remember the trigonometric values given in the above table, follow the below steps:

First divide the numbers 0,1,2,3, & 4 by 4 và then take the positive roots of all those numbers.Hence, we get the values for sine ratios,i.e., 0, ½, 1/√2, √3/2, và 1 for angles 0°, 30°, 45°, 60° and 90°Now, write the values of sine degrees in reverse order to get the values of cosine for the same angles.As we know, tan is the ratio of sin & cos, such as rã θ = sin θ/cos θ. Thus, we can get the values of rã ratio for the specific angles.

Sin Values

sin 0° = √(0/4) = 0

sin 30° = √(1/4) = ½

sin 45° = √(2/4) = 1/√2

sin 60° = √3/4 = √3/2

sin 90° = √(4/4) = 1

Cos Values

cos 0° = √(4/4) = 1

cos 30° = √(3/4) = √3/2

cos 45° = √(2/4) = 1/√2

cos 60° = √(1/4) = 1/2

cos 90° = √(0/4) = 0

Tan Values

tan 0° = 0/1 = 0

tan 30° = (1/2) / (√3/2) = 1/√3

tan 45° = (1/√2) / (1/√2) = 1

tan 60° = <(√3/2)/(½)> = √3

tan 90° = 1/0 = ∞

Hence, the sin cos rã values are found.

Solved Examples

Example 1:

Find the value of (sin 30° + cos 30°) – (sin 60° + cos 60°).

Solution:

We know that,

sin 30° = 1/2

cos 30° = √3/2

sin 60° = √3/2

cos 60° = 1/2

Now,

(sin 30° + cos 30°) – (sin 60° + cos 60°)

= <(1/2) + (√3/2)> – <(√3/2) + (1/2)>

= (1/2) + (√3/2) – (√3/2) – (1/2)

= 0

Example 2:

If A = 30°, prove that chảy 2A = 2 tan A/(1 – tan2A).

Solution:

Given,

A = 30°

tan 2A = chảy 2(30°) = tung 60°

As we know, tung 60° = √3.

So, rã 2A = √3

Now, 

2 chảy A/(1 – tan2A)

= <2 tung 30°/(1 – tan2(30°)>

= <2(1/√3)>/ <1 – (1/√3)2>

= (2/√3)/ <(3 – 1)/3>

= 3/√3

= √3

Therefore, tan 2A = 2 tan A/(1 – tan2A)

Hence proved.

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Practice Problems

Calculate the value of (1/2) cos 45° + tung 60° + (2/3) sin 30°.Find the value of x if cos x = 2 sin 45° cos 45° – sin 30°.Write the values of cos 30°, sin 30°, cos 90°, chảy 45°, sin 45°, & sin 90°.


Frequently Asked Questions – FAQs


What are the values of sin, cos and tan for the angle of 60°?


The values of sin, cos và tan for 60° are given by:sin 60° = √3/2cos 60° = 1/2tan 60° = √3