Use this cos calculator to easily calculate the cosine of an angle given in degrees or radians. The cosine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the adjacent side to the hypotenuse.

It is the complement to the sine. The cosine of a degree angle is equal to zero, since in order to calculate it we would need a triangle with two degree angles, which is the definition of a straight line. As the third side of the triangle does not exist length is 0the cosine equals zero 0 divided by the length of the hypotenuse equals 0. You can use this cosine calculator to verify this.

The reciprocal of cosine is the secant: sec xsometimes written as secant xwhich gives the ratio of the length of the hypotenuse to the length of the side opposite to the angle. The inverse of the cosine is the arccosine function: acos x or arccos xwhich takes values between 0 and degrees. It is useful for finding an angle x when cos x is known. Our cosine calculator supports input in both degrees and radians, so once you have measured the angle, or looked up the plan or schematic, you just input the measurement and press "calculate".

This is how easy it is. If the angle is unknown, but the lengths of the adjacent side and the hypotenuse of a right angle triangle are given, then calculating the cosine can be done by dividing the adjacent side by the hypotenuse side c as per the figure above. The cosine function can be used to model periodic phenomena in physics, biology, social sciences, etc.

A more practical example is if you want to cut down a tree and you know its height and want to know how far from it you are currently standing, use the tan function. JPEG, a very common image compression algorithm, uses so-called "discrete cosine transform" function DCT to express finite sequences of data points as sums of cosine functions with different oscillation frequencies.

Above: a wave generated using the cosine function. A cosine wave is the mirror image of a sine wave. If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.

## How to Calculate the Cosine of an Angle

Calculators Converters Randomizers Articles Search. Cosine Calculator Use this cos calculator to easily calculate the cosine of an angle given in degrees or radians.

Szafir odnowienie certyfikatu instrukcjaShare calculator:. Embed this tool! Related calculators Sine Calculator Arccosine Calculator. The Cosine function cos x The cosine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the adjacent side to the hypotenuse.This trigonometry calculator will help you in two popular cases when trigonometry is needed. If you want to find the values of sine, cosine, tangent and their reciprocal functions, use the first part of the calculator.

Searching for the missing side or angle in a right triangleusing trigonometry? Our tool is also a safe bet! Type given values in the second part of the calculator and in a blink of an eye you'll find the answer. Scroll down if you want to read more about what is trigonometry and where you can apply it. There are many other tools useful when dealing with trigonometry problems. Check out two popular trigonometric laws: law of sines and law of cosines calculators, helping to solve any kind of a triangle.

If you want to read more about the trigonometric functions, go to our dedicated tools:. Trigonometry is a branch of mathematics. As the name suggests, trigonometry deals mostly with angles and triangles ; in particular, it's defining and using the relationships and ratios between angles and sides in triangles.

The primary application is thus solving triangles, specifically right triangles, but also any other type of triangle you like. Trigonometry has plenty of applications: from everyday life problems such as calculating the height or distance between objects to the satellite navigation system, astronomy, and geography.

Also, sine and cosine functions are fundamental for describing periodic phenomena - thanks to them, we can describe oscillatory movements as simple pendulum and waves like sound, vibration or light. Many different fields of science and engineering use trigonometry and trigonometric functions, to mention only a few of them: music, acoustics, electronics, medicine and medical imaging, biology, chemistry, meteorology, electrical, mechanical and civil engineering, even economics The trigonometric functions are really all around us!

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.

Additionally, if the angle is acute, the right triangle will be displayed, which can help you in understanding how the functions may be interpreted. To find the missing sides or angles of the right triangle, all you need to do is enter the known variables into the trigonometry calculator.

You need only two given values in the case of:.

Amplificador kicker impulse ix252Remember that if you know two angles, it's not enough to find the sides of the triangle. Two triangles having the same shape which means they have equal angles may be of different sizes not the same side length - that kind of relationship is called triangle similarity.

If the sides have the same length, then the triangles are congruent. Trigonometry is the study of the relationships within a triangle. For right angled triangles, the ratio between any two sides is always the same, and are given as the trigonometry ratios, cos, sin, and tan.

Trigonometry can also help find some missing triangular informatione. Trigonometry can be hard at first, but after some practise you will master it! Here are some trigonometry tips: label the hypotenuse, adjacent and opposite on your triangle to help you figure out what identity to use, and remember the mnemonic SOHCAHTOA for the trigonometric relationships!The other is the isosceles right triangle. They are special because, with simple geometry, we can know the ratios of their sides.

For the definition of measuring angles by "degrees," see Topic Theorem 6. For, 2 is larger than. The cited theorems are from the Appendix, Some theorems of plane geometry. Here are examples of how we take advantage of knowing those ratios. Example 1.

## Trigonometric Ratios of Special Angles: 0°, 30°, 45°, 60°, 90°

The student should sketch the triangle and place the ratio numbers. Problem 1. To see the answer, pass your mouse over the colored area. To cover the answer again, click "Refresh" "Reload". The sine is the ratio of the opposite side to the hypotenuse.

The tangent is ratio of the opposite side to the adjacent. Problem 2.

Scuola in chiaro miur codice meccanograficoThe cotangent is the ratio of the adjacent side to the opposite. As for the cosine, it is the ratio of the adjacent side to the hypotenuse. Before we come to the next Example, here is how we relate the sides and angles of a triangle:.

If an angle is labeled capital A, then the side opposite will be labeled small a. Similarly for angle B and side bangle C and side c. Example 3. To solve a triangle means to know all three sides and all three angles. Whenever we know the ratios of the sides, we can solve the triangle by the method of similar figures.

Therefore every side will be multiplied by 5. Therefore, side b will be 5 cm. And it has been multiplied by 5. It will be 5 cm. Whenever we know the ratio numbers, the student should use this method of similar figures to solve the triangle, and not the trigonometric Table.

Problem 3. How long are sides d and f? The student should draw a similar triangle in the same orientation. Then see that the side corresponding to was multiplied by. Therefore, each side will be multiplied by. Side f will be 2.

**Trick for doing trigonometry mentally!**

Problem 4. How long are sides p and q? The side corresponding to 2 has been divided by 2. Therefore, each side must be divided by 2.These values are used very often and it is recommended from my point of view that student should be able to tell the values instantly when asked.

In this post our motive is to learn how to fill the table. Once, you learn to fill this table, you would be able to calculate any value in your mind. Just memorize the values for sin 0sin 30sin 45sin 60 and sin Even there is no need to try too hard to memorize them. There is an easy way to memorize them. Note down the pattern from sin 0 to sin 90 :. All the cos values are filled in opposite order starting from sin 0 to sin I mean to say that.

Hence, all the tan values can be obtained from sin and cos values. Xerus Manually there is no easy technique to find value of degrees or degrees. Technology can be used to find these values. Trigonometry is about right angled triangles which is 90 degree if u r saying then it means a circle. I was struggling for a long time to learn the trignometrical values. This information was very helpful.

Very easy method. I don't understand one thing.

### Precalculus Examples

Further more regardless of which side we take tangent of 90 degrees would still be defined so how can tan 90 not be defined? Here, perpendicular is the opposite side from angle x and base is adjacent side from angle x, please note: we don't take hypotenuse as adjacent or perpendicular.

Because Tan 90 would mean both Theta and the right angle are 90 degrees and therefore the third angle would be 0 degrees which isn't possible.

And at 90 degrees, inside a circle, the Y axis value in a unit circle is 1 and the x axis value in a unit circle is 0 and any fraction where the denominator is zero is undefined. Also it can become clear if you look at the tan's graph, it goes on increasing at 90 and degrees.

It's an amazing trick. I was struggling hard to learn this but you made it very easy thanx a lot pls upload all maths formulas.

This process is known to me as I'm a teacher in maths.Enter a problem Precalculus Examples Popular Problems. Use the definition of cosine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values. Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.

Replace the known values in the equation. Raise to the power of. Multiply by. Pull terms out from under the radical, assuming positive real numbers. Find the value of sine. Use the definition of sine to find the value of. Substitute in the known values. Find the value of tangent. Use the definition of tangent to find the value of. Find the value of cotangent. Use the definition of cotangent to find the value of. Find the value of secant.

Use the definition of secant to find the value of. Find the value of cosecant. Use the definition of cosecant to find the value of. This is the solution to each trig value. This website uses cookies to ensure you get the best experience on our website. More Information.By Yang Kuang, Elleyne Kase.

Alu zinc spray soudalBecause you spend a ton of time in pre-calculus working with trigonometric functions, you need to understand ratios. One important ratio in right triangles is the cosine. The cosine of an angle, or. Consider this example: A ladder leans against a building, creating an angle of 75 degrees with the ground. The base of the ladder is 3 feet away from the building.

Brakes squeaking on new carHow long is the ladder? No problem! The right angle goes between the building and the ground, because otherwise the building would be crooked and fall down.

Because you know where the right angle is, you know that the hypotenuse is the ladder itself. The given angle is down on the ground, which means the opposite leg is the distance on the building from where the top of the ladder touches it to the ground.

The third side, the adjacent leg, is the distance the bottom of the ladder rests from the building. You have. Why do you use 75 degrees in the cosine function? Because you are told that the angle the ladder makes with the ground is 75 degrees. Now divide both sides by cos 75 degrees to isolate x; you get. The cos 75 degrees is just a number. When you plug it into your calculator, you get a decimal answer make sure you set your calculator to degree mode before attempting to do this problem.

Mary Jane Sterling aught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois for more than 30 years. How to Calculate the Cosine of an Angle.

One ladder plus one building equals one cosine problem. About the Book Author Mary Jane Sterling aught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois for more than 30 years.Scroll down the page if you need more examples and explanations on how to derive and use the trig ratios of special angles.

How to derive the trigonometric function values of 30, 45 and 60 degrees and their corresponding radian measure. This video shows how to find the trig ratios of the special angles: sine, cosine and tangent values of 0, 30, 45, 60 and 90 degrees.

Scroll down the page for part 2. How to use the trig ratios of special angles to find exact values of expressions involving sine, cosine and tangent values of 0, 30, 45, 60 and 90 degrees? A pattern to help you remember the Sine and Cosines of Special Angles in the first quadrant. This is Part 1. Example: Find cos 90, tan 90, sinsintansintan Example: Find coscotsinseccsccossin Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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Trigonometric Function Values Of Special Angles How to derive the trigonometric function values of 30, 45 and 60 degrees and their corresponding radian measure.

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