without using calculator,
find the Value of following is
cosec(-38888)
To find the value of cosec(-38888) without using a calculator, we can first determine the reference angle, which is the positive acute angle with the same trigonometric value.
Since cosec is the reciprocal of the sine function, we can calculate the sine of the reference angle and then take its reciprocal to find the cosecant.
1. Start by finding the reference angle:
a. Divide the given angle by 360 (since one full revolution is 360 degrees):
-38888 / 360 = -108 with a remainder of 32
b. The negative sign doesn't affect the reference angle, so we ignore it: 108
c. The reference angle is 32 degrees since the remainder is 32.
2. Calculate the sine of the reference angle:
a. Convert the reference angle to radians by multiplying by π/180:
32 * π/180 ≈ 0.5585 radians
b. Determine the sine of the reference angle using the unit circle or trigonometric identities:
sin(0.5585) ≈ 0.5331
3. Finally, take the reciprocal of the sine to find the cosecant:
cosec(-38888) ≈ 1 / 0.5331 ≈ 1.874
Therefore, the value of cosec(-38888) is approximately 1.874.