Examples on Sin 2x Formula
Example 1. If sin x = 3/5, find the value of sin 2x using the formula.
Solution:
We have, sin x = 3/5.
Clearly, cos x = 4/5.
Using the formula we get,
sin 2x = 2 sin x cos x
⇒ sin 2x = 2 (3/5) (4/5)
⇒ sin 2x = 24/25
Example 2. If cos x = 12/13, find the value of sin 2x using the formula.
Solution:
We have, cos x = 12/13.
Clearly, sin x = 5/13.
Using the formula we get,
sin 2x = 2 sin x cos x
sin 2x = 2 (5/13) (12/13)
sin 2x = 120/169
Example 3. If tan x = 12/5, find the value of sin 2x using the formula.
Solution:
We have, tan x = 12/5.
Using the formula we get,
sin2x = (2tan x)/(1 + tan2x).
⇒ sin 2x = 2 × (12/5) / {1 + (12/5)2}
⇒ sin 2x = 120/169
Example 4. If cosec x = 17/8, find the value of sin 2x using the formula.
Solution:
We have, cosec x = 17/8.
Clearly sin x = 8/17 and cos x = 15/17.
Using the formula we get,
sin 2x = 2 sin x cos x
⇒ sin 2x = 2 (8/17) (15/17)
⇒ sin 2x = 240/289
Example 5. If cot x = 15/8, find the value of sin 2x using the formula.
Solution:
We have, cot x = 15/8
tan x = 1 / cot x = 1 / (15/8)
⇒ tan x = 8 / 15
Using the formula we get,
sin2x = (2tan x)/(1 + tan2x).
⇒ sin 2x = 2 × (18 / 15) / {1 + (18 / 15)2}
⇒ sin 2x = 240/289
Example 6. If cosec x = 13/12, find the value of sin 2x using the formula.
Solution:
We have, cosec x = 13/12.
Clearly sin x = 12/13 and cos x = 5/13 (using pythagoras theorem)
Using the formula we get,
sin 2x = 2 sin x cos x
⇒ sin 2x = 2 (12/13) (5/13)
⇒ sin 2x = 120/169
Example 7. If sec x = 5/3, find the value of sin 2x using the formula.
Solution:
We have, sec x = 5/3.
Clearly cos x = 3/5 and sin x = 4/5 (using pythagoras theorem)
Using the formula we get,
sin 2x = 2 sin x cos x
⇒ sin 2x = 2 (4/5) (3/5)
⇒ sin 2x = 24/25
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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