Easy way to learn sin cos tan formulas. We will discuss two methods to learn sin cos and tang formulas easily. Students need to remember two words and they can solve all the problems about sine cosine and tangent. You can learn easily formula of sin cos and tan by learning word SOHCAHTOA.So now we disucss how it works to remember the. Trig calculator finding sin, cos, tan, cot, sec, csc To find the trigonometric functions of an angle, enter the chosen angle in degrees or radians. Underneath the calculator, six most popular trig functions will appear - three basic ones: sine, cosine and tangent, and their reciprocals: cosecant, secant and cotangent. The basic trigonometric functions include the following (6 ) functions: sine ( left( sin x right), ) cosine ( left( cos x right), ) tangent ( left( tan x right. Cosine is just like Sine, but it starts at 1 and heads down until π radians (180°) and then heads up again. Plot of Sine and Cosine In fact Sine and Cosine are like good friends: they follow each other, exactly π /2 radians (90°) apart.

• Sin Cos Tan Sec Csc Cot
• When To Use Cos Or Sin
• Sin Cos Tan Table
• How To Find Sin Cos Tan
• Sin Cos Tan 90
• Tan Cos Csc

To better understand certain problems involving aircraftand propulsionit is necessary to use some mathematical ideas fromtrigonometry,the study of triangles.Let us begin with some definitions and terminologywhich we will use on this slide.A right triangle is athree sided figure with one angle equal to 90 degrees. A 90 degree angle iscalled a right angle which gives the right triangle its name.We pick one of the two remaining angles and label it cand the third angle we label d.The sum of the angles of any triangle is equal to 180 degrees.If we know the value of c,we then know that the value of d:

90 + c + d = 180

d = 180 - 90 - c

d = 90 - c

We define the side of the triangle opposite from the right angle tobe the hypotenuse. It is the longest side of the three sidesof the right triangle. The word 'hypotenuse' comes from two Greek wordsmeaning 'to stretch', since this is the longest side.We label the hypotenuse with the symbol h.There is a side opposite the angle c which we label ofor 'opposite'. The remaining side we label a for 'adjacent'.The angle c is formed by the intersection of the hypotenuse hand the adjacent side a.

We are interested in the relations between the sides and the angles ofthe right triangle.Let us start with some definitions.We will call theratioof the opposite side of a right triangle to the hypotenusethe sine and give it the symbol sin.

sin = o / h

The ratio of the adjacent side of a right triangle to the hypotenuse is called thecosine and given the symbol cos.

cos = a / h

Finally, the ratio of the opposite side to the adjacent side is called thetangent and given the symbol tan.

tan = o / a

We claim that the value of each ratio depends only on the value ofthe angle c formed by the adjacent and the hypotenuse.To demonstrate this fact,let's study the three figures in the middle of the page.In this example, we havean 8 foot ladder that we are going to lean against a wall. The wall is8 feet high, and we have drawn white lines on the walland blue lines along the ground at one foot intervals.The length of the ladder is fixed.If we incline the ladder so that its base is 2 feet from the wall,the ladder forms an angle of nearly 75.5 degrees degrees with the ground.The ladder, ground, and wall form a right triangle. The ratio of the distance from thewall (a - adjacent), to the length of the ladder (h - hypotenuse), is 2/8 = .25.This is defined to be the cosine of c = 75.5 degrees. (Onanother pagewe will show that if the ladder was twice as long (16 feet),and inclined at the same angle(75.5 degrees), that it would sit twice asfar (4 feet) from the wall. The ratio stays the same for any right trianglewith a 75.5 degree angle.)If we measure the spot on the wall where the ladder touches (o - opposite), the distance is7.745 feet. You can check this distance by using thePythagorean Theoremthat relates the sides of a right triangle:

h^2 = a^2 + o^2

o^2 = h^2 - a^2

o^2 = 8^2 - 2^2

o^2 = 64 - 4 = 60

o = 7.745

The ratio of the opposite to the hypotenuse is .967 and defined to be thesine of the angle c = 75.5 degrees.

Now suppose we incline the 8 foot ladder so that its base is 4 feet from the wall.As shown on the figure, the ladder is now inclined at a lower angle than in thefirst example. The angle is 60 degrees, and the ratio of the adjacent tothe hypotenuse is now 4/8 = .5 . Decreasing the angle cincreases the cosine of the angle because the hypotenuse is fixedand the adjacent increases as the angle decreases. If we incline the 8 footladder so that its base is 6 feet from the wall, the angle decreases toabout 41.4 degrees and the ratio increases to 6/8, which is .75.As you can see, for every angle,there is a unique point on the ground that the 8 foot ladder touches,and it is the same point every time we set the ladder to that angle.Mathematicians call this situation afunction.The ratio of the adjacentside to the hypotenuse is a function of the angle c, so we can write thesymbol as cos(c) = value.

Notice also that as the cos(c) increases, the sin(c) decreases.If we incline the ladder so that the base is 6.938 feet from the wall,the angle c becomes 30 degrees and the ratio of the adjacent tothe hypotenuse is .866.Comparing this result with example two we find that:

cos(c = 60 degrees) = sin (c = 30 degrees)

sin(c = 60 degrees) = cos (c = 30 degrees)

We can generalize this relationship:

sin(c) = cos (90 - c)

90 - c is the magnitude of angle d. That is why wecall the ratio of the adjacent and the hypotenuse the 'co-sine' of the angle.

sin(c) = cos (d)

Since the sine, cosine, and tangent are all functions of the angle c, we candetermine (measure) the ratios once and produce tables of the values of thesine, cosine, and tangent for various values of c. Later, if we know thevalue of an angle in a right triangle, the tables will tell us the ratioof the sides of the triangle.If we know the length of any one side, we can solve for the length of the othersides.Or if we know the ratio of any two sides of a right triangle, we canfind the value of the angle between the sides.We can use the tables to solve problems.Some examples of problems involving triangles and angles include theforces on an aircraft in flight,the application oftorques,and the resolution of thecomponentsof a vector.

Here are tables of the sine, cosine, and tangent which you can use to solveproblems.

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Beginner's Guide Home Page

You might like to read about Trigonometry first!

Right Triangle

The Trigonometric Identities are equations that are true for Right Angled Triangles. (If it is not a Right Angled Triangle go to the Triangle Identities page.)

Each side of a right triangle has a name:

Adjacent is always next to the angle

And Opposite is opposite the angle

We are soon going to be playing with all sorts of functions, but remember it all comes back to that simple triangle with:

• Angle θ
• Hypotenuse
• Adjacent
• Opposite

Sine, Cosine and Tangent

The three main functions in trigonometry are Sine, Cosine and Tangent.

They are just the length of one side divided by another

For a right triangle with an angle θ :

cos(θ) = Adjacent / Hypotenuse

When we divide Sine by Cosine we get: sin(θ)cos(θ) = Opposite/HypotenuseAdjacent/Hypotenuse = OppositeAdjacent = tan(θ) So we can say: tan(θ) = sin(θ)cos(θ) That is our first Trigonometric Identity. Cosecant, Secant and Cotangent We can also divide 'the other way around' (such as Adjacent/Opposite instead of Opposite/Adjacent): sec(θ) = Hypotenuse / Adjacent sin(θ) = 2/4, and csc(θ) = 4/2 Because of all that we can say: sin(θ) = 1/csc(θ) cos(θ) = 1/sec(θ) tan(θ) = 1/cot(θ) And the other way around: csc(θ) = 1/sin(θ) sec(θ) = 1/cos(θ) cot(θ) = 1/tan(θ) And we also have: Pythagoras Theorem For the next trigonometric identities we start with Pythagoras' Theorem: The Pythagorean Theorem says that, in a right triangle, the square of a plus the square of b is equal to the square of c: a2 + b2 = c2 Dividing through by c2 gives Sin Cos Tan Sec Csc Cot a2c2 + b2c2 = c2c2 This can be simplified to: (ac)2 + (bc)2 = 1 Now, a/c is Opposite / Hypotenuse, which is sin(θ) And b/c is Adjacent / Hypotenuse, which is cos(θ) So (a/c)2 + (b/c)2 = 1 can also be written: sin2 θ + cos2 θ = 1 Note: sin2 θ means to find the sine of θ, then square the result, and sin θ2 means to square θ, then do the sine function Example: 32° Using 4 decimal places only: sin(32°) = 0.5299... cos(32°) = 0.8480... Now let's calculate sin2 θ + cos2 θ: 0.52992 + 0.84802 = 0.2808... + 0.7191... = 0.9999... We get very close to 1 using only 4 decimal places. Try it on your calculator, you might get better results! Related identities include: sin2 θ = 1 − cos2 θ cos2 θ = 1 − sin2 θ tan2 θ + 1 = sec2 θ tan2 θ = sec2 θ − 1 cot2 θ + 1 = csc2 θ cot2 θ = csc2 θ − 1 How Do You Remember Them? The identities mentioned so far can be remembered using one clever diagram called the Magic Hexagon: But Wait ... There is More! There are many more identities ... here are some of the more useful ones: Opposite Angle Identities sin(−θ) = −sin(θ) cos(−θ) = cos(θ) tan(−θ) = −tan(θ) Double Angle Identities When To Use Cos Or Sin Half Angle Identities Note that '±' means it may be either one, depending on the value of θ/2 Sin Cos Tan Table Angle Sum and Difference Identities Note that means you can use plus or minus, and the means to use the opposite sign. How To Find Sin Cos Tan sin(A B) = sin(A)cos(B) cos(A)sin(B) Sin Cos Tan 90 cos(A B) = cos(A)cos(B) sin(A)sin(B) tan(A B) = tan(A) tan(B)1 tan(A)tan(B) Tan Cos Csc cot(A B) = cot(A)cot(B) 1cot(B) cot(A) Triangle Identities There are also Triangle Identities which apply to all triangles (not just Right Angled Triangles)