Trigonometry Relations Calculator: This calculator determines trigonometry calculations (sin,cos,tan,csc,sec,cot) based on various measures that you enter. Simply enter the measurements you know and press the button.

The inverse trigonometric functions (sin-1, cos-1, and tan-1) allow you to find the measure of an angle in a right triangle.All that you need to know are any two sides as well as how to use SOHCAHTOA.
Use SOHCAHTOA and set up a ratio such as sin(16) = 14/x. (From here solve for X).By the way, you could also use cosine. Set up the following equation using the Pythagorean theorem: x 2 = 48 2 + 14 2.

by M. Bourne

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For the angle θ in a right-angled triangle as shown, we name the sides as:

hypotenuse (the side opposite the right angle)
adjacent (the side 'next to' θ)
opposite (the side furthest from the angle θ)

We define the three trigonometrical ratios sine θ, cosine θ, and tangent θ as follows (we normally write these in the shortened forms sin θ, cos θ, and tan θ):

Sin Cos Tan Calculator

Download driver tp link tl wn422g 54mbps windows xp. `sin theta=text(opposite)/text(hypotenuse)` `cos theta =text(adjacent)/text(hypotenuse)``tan theta =text(opposite)/text(adjacent)`

To remember these, many people use SOH CAH TOA, that is:

Sin θ = Opposite/Hypotenuse,

Cos θ = Adjacent/Hypotenuse, and

Tan θ = Opposite/Adjacent

The Reciprocal Trigonometric Ratios

Often it is useful to use the reciprocal ratios, depending on the problem. (In plain English, the reciprocal of a fraction is found by turning the fraction upside down.)

`'cosecant' θ` is the reciprocal of `'sine' θ`,

`'secant' θ` is the reciprocal of `'cosine' θ`, and

`'cotangent' θ` is the reciprocal of `'tangent' θ`

We usually write these in short form as `csc θ`, `sec θ` and `cot θ`. (In some textbooks, 'csc' is written as 'cosec'. It's the same thing.)

`csc theta =text(hypotenuse)/text(opposite)` `sec theta =text(hypotenuse)/text(adjacent)` `cot theta =text(adjacent)/text(opposite)`

Important note: There is a big difference between csc θ and sin^-1 θ.

The first one is a reciprocal: `csc theta=1/(sin theta)`.
The second one involves finding an angle whose sine is θ.

So on your calculator, don't use your sin^-1 button to find csc θ.

We will meet the idea of sin^-1θ in the next section, Values of Trigonometric Functions.

The Trigonometric Functions on the x-y Plane

Sin Cos Tan Chart

For an angle in standard position, we define the trigonometric ratios in terms of x, y and r:

`sin theta =y/r` `cos theta =x/r``tan theta =y/x`

Notice that we are still defining

sin θ as `'opp'/'hyp'`;

cos θ as `'adj'/'hyp'`, and

Sin Cos Tan Calculator

tan θ as `'opp'/'adj'`,

but we are using the specific x-, y- and r-values defined by the point (x, y) that the terminal side passes through. We can choose any point on that line, of course, to define our ratios.

To find r, we use Pythagoras' Theorem, since we have a right angled triangle:

`r=sqrt(x^2+y^2)`

Not surprisingly, the reciprocal ratios are defined similarly in terms of the x-, y- and r-values as follows:

`csc theta =r/y` `sec theta =r/x``cot theta =x/y`

Sin Calculator

We will see some examples of finding exact values in the next section, Values of Trigonometric Functions ».