1.3.5 Describe the shift of a sine or cosine graph from the equation of the function.

1.3.4 Identify the graphs and periods of the trigonometric functions.

1.3.3 Write the basic trigonometric identities.

1.3.2 Recognize the triangular and circular definitions of the basic trigonometric functions.

1.3.1 Convert angle measures between degrees and radians.

In trigonometry, quotient identities refer to trigonometric identities that are divided by each other whereas reciprocal identities are ones that are the multiplicative inverses of the trigonometric functions. What is the Difference Between Quotient and Reciprocal Identities? The cosecant function is the reciprocal of the sine function.

The reciprocal identity of sin x is cosec x because sin x = 1/cosec x. What is the Reciprocal Identity of Sin x? If you find a way to multiply each side of an equation by a trigonometric function's reciprocal, you may be able to reduce some part of the equation and simplify it. The reciprocal identities are very useful when solving trigonometric equations.

The secant function is the reciprocal of the cosine function. The reciprocal identity of cos x is sec x because cos x = 1/sec x. What is the Reciprocal Identity of Cos x? The formulas of the six main reciprocal identities are: The sine function is the reciprocal of the cosecant function and vice-versa the cosine function is the reciprocal of the secant function and vice-versa cotangent function is the reciprocal of the tangent function and vice-versa. The reciprocals of the six fundamental trigonometric functions (sine, cosine, tangent, secant, cosecant, cotangent) are called reciprocal identities. Hence, we haveįAQs on Reciprocal Identities What are Reciprocal Identities in trigonometry? tan θ = sin θ/cos θ and cot θ = cos θ/sin θ ⇒ tan θ is the reciprocal of cot θ and cot θ is the reciprocal of tan θ. cos θ = Base/Hypotenuse = b/a and cosec θ = Hypotenuse/Base = a/b ⇒ cos θ is the reciprocal of sec θ and sec θ is the reciprocal of cos θ. Similarly, we will prove other reciprocal identities.

We know that sin θ = Perpendicular/Hypotenuse = c/a and cosec θ = Hypotenuse/Perpendicular = a/c ⇒ sin θ is the reciprocal of cosec θ and cosec θ is the reciprocal of sin θ.

Consider a right-angled triangle ABC with a right angle at C. First, we will derive the reciprocal identity of the sine function. Now, that we know the reciprocal identities of trigonometry, let us now prove each one of them using the definition of the basic trigonometric functions.

Sin cos tan examples