Find the values of the six trigonometric functions for angle θ calculator

Trigonometric Ratios

Table of Contents Show

How to Use the Trigonometric Ratios Calculator?
What is Meant by Trigonometric Ratios?
Right triangle calculator
Trigonometric functions calculator
Triginometric expression calculator
Trigonometric functions
Trigonometric Functions Tutorial
What are the 6 trigonometric functions calculator?
What are the six trigonometric functions of θ?
What is the value of angle θ?

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

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

What are the 6 trigonometric functions calculator?

Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent.

What are the six trigonometric functions of θ?

Thus, for each θ, the six ratios are uniquely determined and hence are functions of θ. They are called the trigonometric functions and are designated as the sine, cosine, tangent, cotangent, secant, and cosecant functions, abbreviated sin, cos, tan, cot, sec, and csc, respectively.

What is the value of angle θ?

The sine of the angle θ is represented by the y-value of the point P on the unit circle. Thus, since sin θ = sin (180 − θ), we mark the two equal intervals in the graph. Hence, between 0° and 180°, the graph is symmetric about θ = 90°. Similarly, between 180° and 360°, the graph is symmetric about θ = 270°.