If theta nearest to zero.than value of sin theta and cos theta will be...
When theta(Q) is very small then,SinQ ~ Q.tanQ ~ Q. CosQ ~ 1- Q^2/2.You can understand it by the expansion of cosQ, sinQ and tan Q.
If theta nearest to zero.than value of sin theta and cos theta will be...
Value of sin theta when theta is near zero:
When theta is near zero, the value of sin theta can be approximated using the small angle approximation. The small angle approximation states that for small angles, the sine of the angle is approximately equal to the angle itself, measured in radians.
Value of cos theta when theta is near zero:
Similarly, when theta is near zero, the value of cos theta can also be approximated using the small angle approximation. For small angles, the cosine of the angle is approximately equal to 1.
Explanation:
1. Value of sin theta when theta is near zero:
- The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
- When theta is near zero, the opposite side of the right triangle becomes very small compared to the hypotenuse.
- As a result, the value of sin theta approaches zero as theta approaches zero.
- Mathematically, sin theta ≈ theta for small values of theta.
2. Value of cos theta when theta is near zero:
- The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
- When theta is near zero, the adjacent side of the right triangle is almost equal to the hypotenuse.
- Therefore, the value of cos theta approaches 1 as theta approaches zero.
- Mathematically, cos theta ≈ 1 for small values of theta.
Summary:
- When theta is near zero, the value of sin theta can be approximated as theta, and the value of cos theta can be approximated as 1.
- This approximation is based on the small angle approximation, which holds true for small values of theta.
- As theta increases, the actual values of sin theta and cos theta deviate from these approximations.
- It's important to note that these approximations are most accurate for very small angles and may become less accurate as theta increases.
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