What are the 6 trigonometric identities?
John Castro
Published Feb 20, 2026
What are the 6 trigonometric identities?
There are six trigonometric identities that are sine, cosine, tangent, secant, cosecant, and cotangent.
What are the 8 trigonometric identities?
Terms in this set (8)
- Reciprocal: csc(θ) = csc(θ) = 1/sin(θ)
- Reciprocal: sec(θ) = sec(θ) = 1/cos(θ)
- Reciprocal: cot(θ) = cot(θ) = 1/tan(θ)
- Ratio: tan(θ) = tan(θ) = sin(θ)/cos(θ)
- Ratio: cot(θ) = cot(θ) = cos(θ)/sin(θ)
- Pythagorean: sin costs = $1.
- Pythagorean: I tan = get sic.
- Pythagorean: I cut = crescent rolls.
Why are there six trig functions?
The six trigonometric functions are defined as ratios of sides in a right triangle. Their values depend only on the angle and not on any particular right triangle. The other three functions—cosecant, secant, and cotangent—are reciprocals of the first three.
What are the 6 trigonometric ratios and its formulas?
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec)….
| Trigonometric Ratios | |
|---|---|
| Sin θ | Opposite Side to θ/Hypotenuse |
| Cot θ | Adjacent Side/Opposite Side & 1/tan θ |
| Sec θ | Hypotenuse/Adjacent Side & 1/cos θ |
What are the 6 functions?
The six main trigonometric functions are sine, cosine, tangent, secant, cosecant, and cotangent.
What are the 9 trigonometric identities?
Sum and Difference of Angles Trigonometric Identities
- sin(α+β)=sin(α). cos(β)+cos(α). sin(β)
- sin(α–β)=sinα. cosβ–cosα. sinβ
- cos(α+β)=cosα. cosβ–sinα. sinβ
- cos(α–β)=cosα. cosβ+sinα. sinβ
- tan(α+β)=tanα+tanβ1–tanα. tanβ ( α + β ) = tan β 1 – tan α .
- tan(α–β)=tanα–tanβ1+tanα. tanβ ( α – β ) = tan β 1 + tan
What are the 3 trig identities?
The three main functions in trigonometry are Sine, Cosine and Tangent….Sine, Cosine and Tangent.
| Sine Function: | sin(θ) = Opposite / Hypotenuse |
|---|---|
| Tangent Function: | tan(θ) = Opposite / Adjacent |
What are the six circular functions?
10.3: The Six Circular Functions and Fundamental Identities
- The cosine of θ, denoted cos(θ), is defined by cos(θ)=x.
- The sine of θ, denoted sin(θ), is defined by sin(θ)=y.
- The secant of θ, denoted sec(θ), is defined by sec(θ)=1x, provided x≠0.
- The cosecant of θ, denoted csc(θ), is defined by csc(θ)=1y, provided y≠0.
Why there are only 6 trigonometric ratios?
There are only 6 trigonometric ratios because only 6 ratios can define ratios of all sides. For example, If you want ratio between perpendicular and hypotenuse there is sin. If you want ratio between perpendicular and base there is tan.
What are the trigonometric functions and identities?
They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, co-secant, tangent and co-tangent. By using a right-angled triangle as a reference, the trigonometric functions and identities are derived: All these are taken from a right angled triangle.
What are the 6 trigonometry functions?
Introduction to the 6 trigonometry functions – sine, cosine, tangent, secant, cosecant, cotangent
What are the periods of trigonometric functions?
Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2 π while tangent and cotangent have period π. Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions.
What ratios are used to find the elements in trigonometry?
There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, co-secant, tangent and co-tangent. By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:
