Trigonometric Ratios
Enter Hypotenuse of the Triangle=
Enter Base of the Triangle=
Enter Perpendicular of the Triangle=
Sinθ= Cosecθ=
Cosθ= Secθ=
Tanθ=
Cotθ=
Trigonometric Ratios Calculator is a free online tool that displays the ratios for six trigonometric ratios. BYJU’S online trigonometric ratios calculator tool makes the calculation faster, and it displays the ratios in a fraction of seconds.
How to Use the Trigonometric Ratios Calculator?
The procedure to use the trigonometric ratios calculator is as follows:
Step 1: Enter the base, perpendicular, and hypotenuse side in the input field
Step 2: Now click the button “Calculate Trigonometric Ratios” to get the result
Step 3: Finally, the ratio value for six functions will be displayed in the new window
What is Meant by Trigonometric Ratios?
In trigonometry, the trigonometric ratios are defined from the sides of a right triangle. There are six trigonometry ratios. The three basic trigonometric ratios are sine, cosine, and tangent. The other three ratios are derived from the above three mentioned ratios. They are cosecant, secant, and cotangent which are the reciprocals of sine, cosine and tangent. The ratios of six important trigonometric functions are:
Sine (sin) = Opposite side/ Hypotenuse
Cosine (cos) = Adjacentside/ Hypotenuse
Tangent (tan)= Opposite side/ Adjacent
Cosecant (csc) = Hypotenuse/Opposite Side
Secant (sec) = Hypotenuse / Adjacent Side
Cotangent (cot) = Adajcent Side/ Opposite Side
Right triangle calculator
Enter one side and second value and press the Calculate button:
Side a
Side b
Side c
Angle A
Angle B
Trigonometric functions calculator
Triginometric expression calculator
Expression with sin(angle deg|rad)/cos(angle deg|rad)/tan(angle deg|rad)/asin()/acos()/atan():
Expression
Result
Trigonometric functions
sin A = opposite / hypotenuse = a / c
cos A = adjacent / hypotenuse = b / c
tan A = opposite / adjacent = a / b
csc A = hypotenuse / opposite = c / a
sec A = hypotenuse / adjacent = c / b
cot A = adjacent / opposite = b / a
See also
- Trigonometric functions
- Sine calculator
- Cosine calculator
- Tangent calculator
- Arcsin calculator
- Arccos calculator
- Arctan calculator
- Degrees to radians conversion
- Radians to degrees conversion
- Degrees to degrees,minutes,seconds
- Degrees,minutes, seconds to degrees
Trigonometric Functions Tutorial
The six trigonometric functions are sin, cos, tan, csc, sec, and cot. These trig functions allow you to find missing sides of triangles. Trig functions are ratios in a right triangle relative to an angle. Sin of an angle is the ratio of the side length opposite to the angle to the hypotenuse length. Cos of an angle is the ratio of the side length adjacent to the angle to the hypotenuse length. Tan is the ratio of the opposite side length to the adjacent side length. Csc is the reciprocal of sin or the ratio of the hypotenuse to the opposite side instead of the opposite side to the hypotenuse. Sec is the reciprocal of cos or the ratio of the hypotenuse to the adjacent side. Cot is the reciprocal of tan or the ratio of the adjacent side to the opposite side. The way these trig functions are used to find missing sides in a right triangle is shown in the example below. If a right triangle has an angle or measure 27 degrees and a hypotenuse of length 88. The sin function will allow you to find the opposite side length of the triangle. The calculation process for this is shown below.
\sin (\text{angleA})=\frac{\text{opposite}}{\text{hypotenuse}}
\sin (\text{angleA})=\frac{(\text{sideA})}{(\text{sideC})}
\sin ((27))=\frac{\text{sideA}}{(88)}
\text{sideA}=\sin (27)\cdot 88
\text{sideA}=39.9511639770801177
Once the opposite side length is known, the cos function can be used to find the adjacent side length of the triangle. The calculation process for this is shown below:
\cos (\text{angleA})=\frac{(\text{sideB})}{(\text{sideC})}
\cos ((27))=\frac{\text{sideB}}{(88)}
\text{sideB}=\cos (27)\cdot 88
\text{sideB}=88\cos (27)
\text{sideB}=78.4085741285763719
Given only two sides of a right triangle it is also possible to find any angles in a right triangle. If given sides only, inverse trigonometric functions must be used to find the angle measures. The inverse trig functions are arcsin, arccos, arctan, arccsc, arcsec, and arccot. The example below demonstrates the process involved in calculating angle measures given two side lengths of a right triangle. If the hypotenuse of a triangle is of length 34 and the side length adjacent to an unknown angle has length 14, the calculation process shown below can be used.
\cos (\text{angleA})=\frac{\text{adjacent}}{\text{hypotenuse}}
\cos (\text{angleA})=\frac{\text{sideB}}{\text{sideC}}
\cos (\text{angleA})=\frac{(14)}{(34)}
\text{angleA}=\cos ^{-1}(\frac{14}{34})
\text{angleA}=65.684260828823524^\circ