Trigonometric Functions Conversion Calculator

Trigonometric Functions Conversion Calculator is a very useful tool that allows you to convert between different trigonometric functions. For example, convert sine to cosine, tangent to secant, etc.

Trig Functions Conversion

Calculate Reset

What are trigonometric functions?

Trigonometric functions are common basic functions in mathematics, used to express the relationship between angles and sides. For example, in a right triangle, the ratio of the opposite side of an acute angle to the hypotenuse represents the sine, and the ratio of the opposite side of the acute angle to the adjacent side is the tangent. Different trigonometric ratios represent different trigonometric functions. There are six commonly used trigonometric functions, namely, sine, cosine, tangent, cotangent, secant and cosecant. They have a wide range of uses in fields such as nautical, engineering, physics and more.

Why do you need trigonometric functions conversion?

As we all know, it is often necessary to convert between different trigonometric functions in practical applications. For example, given the sine of an angle, calculate the cosine of this angle. Or if you know the sine, you need to find the tangent and cotangent. At this time, you urgently need a trigonometric functions converter, which can convert between different trigonometric functions. In this way, as long as the value of one trigonometric function is known, the other trigonometric functions values can be calculated. Next, let’s see how to convert between different trigonometric functions.

How to convert trigonometric functions

Before the conversion of trigonometric functions, combined with a right triangle, the formulas of 6 commonly used trigonometric functions are listed below:

right triangle

Function	Abbreviation	Formula
Sine	sin	sin(α) = oppositehypotenuse
Cosine	cos	cos(α) = adjacenthypotenuse
Tangent	tan	tan(α) = oppositeadjacent
Cotangent	cot	cot(α) = adjacentopposite
Secant	sec	sec(α) = hypotenuseadjacent
Cosecant	csc	csc(α) = hypotenuseopposite

Have you discovered any patterns? Yes. Sine and cosecant are reciprocals of each other, cosine and secant are reciprocals of each other, tangent and cotangent are reciprocals of each other. Therefore, trigonometric functions can be converted to each other. Let’s explore how they are converted.

sine
cos(θ) = √(1 - sin²(θ))
tan(θ) = sin(θ)√(1 - sin²(θ))
cot(θ) = √(1 - sin²(θ))sin(θ)
sec(θ) = 1√(1 - sin²(θ))
csc(θ) = 1sin(θ)

cosine
sin(θ) = √(1 - cos²(θ))
tan(θ) = √(1 - cos²(θ))cos(θ)
cot(θ) = cos(θ)√(1 - cos²(θ))
sec(θ) = 1cos(θ)
csc(θ) = 1√(1 - cos²(θ))

tangent
sin(θ) = tan(θ)√(1 + tan²(θ))
cos(θ) = 1√(1 + tan²(θ))
cot(θ) = 1tan(θ)
sec(θ) = √(1 + tan²(θ))
csc(θ) = √(1 + tan²(θ))tan(θ)

cotangent
sin(θ) = 1√(1 + cot²(θ))
cos(θ) = cot(θ)√(1 + cot²(θ))
tan(θ) = 1cot(θ)
sec(θ) = √(1 + cot²(θ))cot(θ)
csc(θ) = √(1 + cot²(θ))

secant
sin(θ) = √(sec²(θ) - 1)sec(θ)
cos(θ) = 1sec(θ)
tan(θ) = √(sec²(θ) - 1)
cot(θ) = 1√(sec²(θ) - 1)
csc(θ) = sec(θ)√(sec²(θ) - 1)

cosecant
sin(θ) = 1csc(θ)
cos(θ) = √(csc²(θ) - 1)csc(θ)
tan(θ) = 1√(csc²(θ) - 1)
cot(θ) = √(csc²(θ) - 1)
sec(θ) = csc(θ)√(csc²(θ) - 1)

For example, sin(θ) = 12, what is sin(θ) to cos(θ)?

First, get the formula for converting sine to cosine

cos(θ) = √(1 – sin²(θ))

Second, substitute the sine value into the formula.

cos(θ) = √(1 – sin²(θ)) = √1 – (14)² = √32

Therefore, sin(θ) = 12, the cos(θ) is √32.

Another example, tan(θ) = 0.25, What are cot(θ) and sec(θ)?

The tangent to cotangent formula is

cot(θ) = 1tan(θ)

So, the cot(θ) is 10.25 = 4

The tangent to secant formula is

sec(θ) = √(1 + tan²(θ))

Substitute tan(θ) = 0.25 into the formula

sec(θ) = √(1 + tan²(θ)) = √1 + 0.25² = 1.03

How to use this Trigonometric Functions Conversion calculator

Trigonometry Conversion Calculator is easy to use, 3 steps:

First, select the conversion type, that is, which trigonometric function is to be converted into other trigonometric functions. Specifically include:

Convert sine to other trigonometric functions
Convert cosine to other trigonometric functions
Convert tangent to other trigonometric functions
Convert cotangent to other trigonometric functions
Convert secant to other trigonometric functions
Convert cosecant to other trigonometric functions

Second, enter the value for the trigonometric function.

Third, click Calculate button to get other trigonometric functions values, or click Reset button to start a new conversion.

FAQS

Q: Is the trigonometric conversion one-to-one?
A: By default, it is 1 to 5, that is, convert one trigonometric function into the remaining 5 trigonometric functions. This reduces your operations, but the result is what you need.

Q: What should I pay attention to when entering the values of trigonometric functions?
A: Please make sure the value is within the range of the trigonometric functions. Such as, the range of sine and cosine is between -1 and 1, the tangent and cotangent ranges are not limited. The absolute value of the range of secant and cosecant is greater than or equal to 1.

Q: How to find cos from sin?
A: Since the square of the sine plus the square of the cosine equals 1, the cosine is equal to √(1-sin²(θ)). Just like the formula we summarized above.

Q: What is sine/cosine equal to?
A: Sine over cosine is equal to tangent.

Q: Can I enter decimals or fractions?
A: Yes, of course.

Conclusion

In conclusion, trigonometric conversions are common and important. With the trigonometric conversion calculator, you can easily convert between different trigonometric functions. Welcome to use.