find the value of : sin18'
Since that is a very small angle, the radian approximation
sin theta = theta (in radians)
can be used.
18' = 18/60 degree = 0.3000 degrees
= 0/3*(pi/180)= pi/600 radians
= 0.00523599..
The true sine of the angle is very nearly the same. The exact value is 0.00523596..
I have seen this question as :
find the exact value of sin 18º
18 = 1/2 of 36
Start with a regular pentagon and draw several of the diagonals.
You will see an abundance of angles of 36º,72º and 108º in similar triangles,
and the diagonals intersect each other in the "golden ratio" which is (1+√5)/2
using the cosine law we can show that
cos 36º = (1+√5)/4 which is 1/2(golden ratio)
cos 36º = 1 - 2sin^2 18º
substituting and solving for sin 18º
I got sin 18º = √[(3-√5)/8]
The question still shows up as "18 minutes" on my (Mac) computer but the symbol for degrees appears in Reiny's answer. C'est la vie
To find the value of sin 18', we can use trigonometric identities and properties to derive it. Here's the step-by-step explanation:
1. Start by converting 18 minutes into degrees. Since there are 60 minutes in a degree, 18' is equivalent to (18 ÷ 60) degrees, which simplifies to 0.3 degrees.
2. Recognize that trigonometric functions usually work with angles measured in radians rather than degrees. So, convert 0.3 degrees into radians. To convert degrees to radians, multiply by π/180. Therefore, 0.3 degrees is equal to (0.3 × π/180) radians.
3. Recall the trigonometric identity for sine: sin(π - x) = sin(x). This identity allows us to find the value of sin for angles greater than π/2.
4. Since 0.3 is less than π/2, we can use the identity sin(x) = sin(π - x) to find the value of sin(0.3). By plugging the value into the identity, we get:
sin(0.3) = sin(π - 0.3)
5. Evaluate sin(π - 0.3) by using a scientific calculator. The value of sin(π - 0.3) is approximately 0.2955.
Therefore, the value of sin 18' is approximately 0.2955.