Sin2x Formula
For the derivation of the sin2x formula, we use the trigonometric identities sin2x + cos2x = 1 and the double angle formula of cosine function cos 2x = 1 – 2 sin2x. Using these identities, sin2x can be expressed in terms of cos2 x and cos2x. Let us derive the formulas:
Sin2x Formula in Terms of Cos x
We know that, using trigonometric identities,
sin2x + cos2x = 1 using the equation and sending cos2x to the left-hand side which changes its sign we get,
sin2x = 1 – cos2x
Sin2x Formula in Terms of Cos 2x
We know that, using the double-angle formula,
cos 2x = 1 – 2sin2x using the equation and separating sin2x to one side we get,
sin2x = (1 – cos 2x) / 2
Therefore, the two basic formulas of sin2x are:
sin2x = 1 – cos2x
sin2x = (1 – cos 2x) / 2
Sin 2x Formula
Sin 2x Formula is among the very few important formulas of trigonometry used to solve various problems in mathematics. It is among the various double-angle formulas used in trigonometry. This formula is used to find the sine of the angle with a double value. Sin is among the primary trigonometric ratios that are given by taking the ratio perpendicular to that of the hypotenuse in a right-angled triangle. The range of sin2x is [-1, 1].
Sine ratio is calculated by computing the ratio of the length of the opposing side of an angle divided by the length of the hypotenuse. It is denoted by the abbreviation sin. The image added below shows a right-angle triangle ABC
If θ is the angle formed between the base and hypotenuse of a right-angled triangle then,
sin θ = Perpendicular/Hypotenuse
In this article we will learn about, Sin 2x Trig Identity, Sin 2x Derivation, Sin 2x Examples and others in detail.
Table of Content
- What is Sin 2x Trig Identity?
- Sin 2x Identity Derivation
- Sin 2x Formula in Terms of Tan
- Sin 2x Formula in Terms of Cos
- Sin 2x Formula in Terms of Sin
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