What is the reciprocal ratio of sine

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Trigonometry is all about triangles or to be more precise about the relation between the angles and sides of a right-angled triangle. In this article, we will be discussing about the ratio of sides of a right-angled triangle with respect to its acute angle called trigonometric ratios of the angle and find the reciprocals of these Trigonometric Ratios. The trigonometric ratios of an acute angle in a right triangle are the relationship between the angle and the length of two sides. The ratios defined below are abbreviated as sin C, cos C, and tan C respectively. Reciprocals of basic trigonometric ratios are the inverse values of the sin, cos, and tan values that are computed by reciprocating the sides required for computing the ratio. You will see that cosec A, sec A, and cot A are respectively, the reciprocals of sin A, cos A, and tan A from the following diagrams and examples.

What is the reciprocal ratio of sine

The reciprocal of sine is the cosecant function. There are six main trigonometric functions namely, sine, cosine, tangent, cotangent, secant, and cosecant. An important thing to note is that the reciprocal of sine is not the inverse function of sine, that is, the cosecant function is not the inverse function of sine. So, we have cosecant which is the reciprocal of sine. In this article, let us learn about the properties of the reciprocal of sine, that is, cosecant, its formula, domain, range , derivative, integral and graph. The reciprocal of the sine function is a trigonometric function , called the cosecant function. The reciprocal of the cosecant function is the sine function itself. The product of the reciprocal of sine and the sine function is always equal to 1. The reciprocal of sine, that is cosecant function is the ratio of the hypotenuse to the perpendicular in a right-angled triangle. Since sine function is the ratio of the lengths of the opposite side to the angle in consideration and hypotenuse in a right-angled triangle , the reciprocal of sine is the ratio of the hypotenuse and the opposite side of a right-angled triangle. In other words, the reciprocal of sine is the ratio of the hypotenuse to the perpendicular in a right-angled triangle. The formula of reciprocal of sine is:. The graph of reciprocal of sine, that is, cosecant is a discontinuous graph. We know that the derivative of sin x is cos x.

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The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, cosecant, out of which the three standard trigonometric ratios are sine, cosine, and tangent. The six trigonometric ratios can be grouped in pairs as reciprocals. The reciprocal identities are the reciprocals of these six trigonometric ratios. Note that reciprocal identities are not the same as inverse trigonometric functions. Reciprocal identities are the reciprocals of the six fundamental trigonometric functions sine, cosine, tangent, secant, cosecant, and cotangent. It is obtained by interchanging the values of numerator and denominator.

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What is the reciprocal ratio of sine

The three basic trigonometric functions occur so often as the denominator of a fraction that it is convenient to give names to their reciprocals. We define three new trigonometric functions as follows. We can find exact values for all six trig functions at a given angle if we know the value of any one of them. Calculators do not have keys for the secant, cosecant, and cotangent functions; instead, we calculate their values as reciprocals.

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Correct Incorrect. So in the video, he's talking about reciprocal ratios. And what's the hypotenuse? Online Tutors. Learn Reciprocal Of Sine with tutors mapped to your child's learning needs. United States. Maths Games. So it's 5. Brain Teasers. That's how my mind works, anyway. Change Language. But hurry up, because the offer is ending on 29th Feb! You can suggest the changes for now and it will be under the article's discussion tab. Work Experiences.

Reciprocal Identities are the reciprocals of the six main trigonometric functions, namely sine, cosine, tangent, cotangent, secant, cosecant. The important thing to note is that reciprocal identities are not the same as the inverse trigonometric functions. Every fundamental trigonometric function is a reciprocal of another trigonometric function.

Trigonometry has many applications in the fields such as engineering and aviation, where calculations of height and distance are involved. I was screwed up by this when I was first learning trig, and it's why I really hate the notation they use to describe these concepts. The product of the reciprocal of sine and the sine function is always equal to 1. That's why you don't see buttons for the other ones on calculators. Squares, definitely - but never negative values. Log in. You will be notified via email once the article is available for improvement. Direct link to shabarish. Posted 8 years ago. Show preview Show formatting options Post answer. Trigonometry is all about triangles or to be more precise about the relation between the angles and sides of a right-angled triangle.