find values of the following T-ratio
1] sin(1)
2] cos(1.7)
3]sin(-2.4)
4]tan(2)
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Answers
Answer:
Sin(1) = 0.84147
Sin(-2.4) = - 0.66855
Cos(1.7) = - 0.13052
Tan(2) = -2.15038
Step-by-step explanation:
When Angle in in radian
We know that
Taylor series of Sin(x) is
Sin(x) = x - x³/3! + x^5 / 5! + ........
Putting x = 1
Sin(1) = 1−1/3!+1/5!−1/7!+⋯.
To find the approximate answer we ignore the all terms from 5th term to onward
That is
Sin(1) = 1−1/3!+1/5!−1/7! = 0.84146825396 ≈ 0.84147
Now
putting "x = -2.4" we get
Sin(-2.4) = - sin(2.4) = - {2.4 - (2.4)³ / 3! + ((2.4)^5) / 5! - ((2.4)^7) / 7!
= - 0.66855058285 ≈ - 0.66855
Now
We know that
Cos(x) = 1 - x²/2! + x^4 / 4! - x^6 / 6! + .....
Putting "x =1.7" and ignore higher terms then 4th term we get
Cos(1.7) = 1 - (1.7)²/2! + (1.7)^4 / 4! - (1.7)^6 / 6! = -0.13052023472 ≈ - 0.13052
Now
We know that
tan(x) = sin(x) / Cos(x)
So
Tan(2) = Sin(2) / Cos(2)
and
Sin(2) = sin(2) = 2 - (2)³ / 3! + (2)^5) / 5! - (2)^7) / 7! = 0.90793650793
and
Cos(2) = 1 - (2)²/2! + (2)^4 / 4! - (2)^6 / 6! = -0.42222222222
Thus
Tan (2) = (0.90793650793) / (-0.42222222222)
= -2.15037593985 ≈ -2.15038
So
Sin(1) = 0.84147
Sin(-2.4) = - 0.66855
Cos(1.7) = - 0.13052
Tan(2) = -2.15038
Always remember that these are approximations.
Answer:
Step-by-step explanation:
1 ) : sin1
= > sin( 180 / π )°
= > sin( 180 x 7 / 22 )°
= > sin( 630 / 11 )°
= > sin( 60 - 30 / 11 )°
By using sin( A - B ) = sinAcosB - sinBcosA
= > sin60°cos( 30 / 11 )° - cos60°sin( 30 / 11 )°
= > [ √(3) / 2 x √{ 1 - sin( 30 / 11 )° } ] - [ 1 / 2 x sin( 30 / 11 )° ]
For small angles, sinA = A in radian( approx )
Therefore, sin( 30 / 11 )° = 30 / 11 x π / 180 = 1 / 21
= > [ √(3) / 2 x √{ 1 - ( 1 / 21 )^2 } ] - ( 1 / 21 x 1 / 2 )
= > [ √( 330 ) / 21 ] - 1 / 42 [ √330 = 18.1659 ]
= > 0.841233 ( approx )
Similarly, in other questions,
• First, we have to convert the radian into degrees.
• Then, we have to break that degree so that one part will be too small.
• After that, apply sin( A + B ) = sinAcosB + sinBcosA or sin( A - B ) = sinAcosB - sinBcosA. Small angle approximation, numeric value of sine of an angle is approximately equal to the value of that angle in radian.
