Trigonometric Ratios Calculator need input data from your side to produce the exact answer in no time. So, provide input values such as Hypotenuse, Opposite Side, and Adjacent side and hit on the calculate button to get the output as early as possible.

**Trigonometric Ratios Calculator: **Are you feeling that calculating the trigonometric ratios using the given values is a difficult task? Not anymore, as we have given a handy free Trigonometric Ratios Calculator that produces instant results. This tool is helpful in giving accurate result by eliminating the difficult calculations and you can also save your time. Also, calculator provides a detailed solution for you to learn and understand the trigonometry concept much better.

In mathematics, trigonometry has a very important role to play. Trigonometric ratios are defined from the sides of right angle. Follow these simple guidelines to check the values of six trigonometric ratios.

- At first, know any two sides of a right angle triangle.
- We know that, Hypotenuse of the right angled triangle = √Adjacent-side
^{2}+ Opposite-side^{2}. - Using the above formula, compute the other side of the triangle.
- Substitute the obtained values in the trigonometric ratio formulae provided below.
- Compute the division operation to get the exact value.

Following are the trigonometric function formulae for the right angled triangle. Have a look at them and use them to solve your questions.

1. Sine (sin) = Opposite side/ Hypotenuse

2. Cosine (cos) = Adjacent side/ Hypotenuse

3. Tangent (tan)= Opposite side/ Adjacent

4. Cotangent (cot) = Adjacent Side/ Opposite Side

5. Secant (sec) = Hypotenuse / Adjacent Side

6. Cosecant (cosec) = Hypotenuse/Opposite Side

**Examples**

**Question 1: If β = 30°, prove that 3 sin β - 4 sin ^{3} β = sin 3β?**

**Solution:**

Given that

β = 30°

L.H.S = 3 sin β - 4 sin^{3} β

= 3 sin (30°) - 4 sin^{3} (30°)

= 3 * (1/2) - 4 * (1/2)^{3}

= 3/2 - 4 * (1/8)

= 3/2 - 1/2

= 1

R.H.S = sin 3β

= sin 3.30°

= sin 90°

= 1

Therefore, L.H.S = R.H.S

3 sin β - 4 sin^{3} β = sin 3β (proved)

**Question 2: If Hypotenuse of the triangle is 15 cm, Opposite side length is 8 cm then, find the trigonometric ratios?**

**Solution:**

Given data is

Hypotenuse = 15 cm

Opposite Side = 8 cm

Hypotenuse = √Adjacent-side^{2} + Opposite-side^{2}

15 = √Adjacent-side^{2} + 8^{2}

15 * 15 = Adjacent-side^{2} + 64

225 - 64 = Adjacent-side^{2}

Adjacent side = √161

= 12.68

Sine (sin) = Opposite side/ Hypotenuse = 8/15 = 0.53

Cosine (cos) = Adjacent side/ Hypotenuse = 12.68/15 = 0.845

Tangent (tan)= Opposite side/ Adjacent = 8/12.68 = 0.6309

Cotangent (cot) = Adjacent Side/ Opposite Side = 12.68/8 = 1.585

Secant (sec) = Hypotenuse / Adjacent Side = 15/12.68 = 1.182

Cosecant (cosec) = Hypotenuse/Opposite Side = 15/8 = 1.875

You can easily find the trigonometric ratios using our calculator by just entering the input and click on calculate to obtain the output. If you are looking for other simple calculators similar to this, then here is our website link Onlinecalculator.guru visit and explore more math concepts.

**1. What are the 3 basic trigonometric ratios?**

There are three basic trigonometric ratios which are sine, cosine, and tangent. For the right angled triangle, sine will be division of length of the opposite side/ hypotenuse, cos is adjacent side/ hypotenuse, and tan is opposite side/ adjacent side.

**2. What are the six basic trigonometric ratios?**

The six trigonometric ratios are sine, cosine, tangent, cosecant, secant and cotangent. These are abbreviated as sin, cos, tan, cosec, sec, and cot. The last three trigonometric ratios are expressed as cot = 1/ tan, sec = 1/cos, cosec = 1/sin.

**3. What are the principles of trigonometry?**

Sine, Cosine and Tangent are the principles of trigonometric functions. Trigonometry is a branch of mathematics that studies relationship between sides and angles of the triangles.

**4. Find the value of 4/3 tan ^{2} 60° + 3 cos^{2} 30° - 2 sec^{2} 30° - 3/4 cot^{2} 60°?**

Given expresion is,

4/3 tan^{2} 60° + 3 cos^{2} 30° - 2 sec^{2} 30° - 3/4 cot^{2} 60°

= 4/3 * (√3)^{2} + 3 * (√3/2)^{2} - 2 * (2√3/3)^{2} - 3/4 * (√3/2)^{2}

= 4/3 * 3 + 3 * 3/4 - 2 * 12/9 - 3/4 * 3/9

=4 + 9/4 - 8/3 - 1/4

4/3 tan^{2} 60° + 3 cos^{2} 30° - 2 sec^{2} 30° - 3/4 cot^{2} 60° = 10/3