Question

The Angel O1 is located in Quadrant I, and cos(O1)=83. What is the value of sin(O1)? Express your answer EXACTLY.

a) sin(O1)=855
b) sin(O1)=555
c) sin(O1)=355
d) sin(O1)=1355

Answer 1

To find the value of sin(O1), we use the Pythagorean identity for trigonometric functions. After calculation, the closest exact value in the given options is 0.555, so the correct answer is b) sin(O1)=555.

Step-by-step explanation:

To determine the value of sin(O1) when given cos(O1)=83 (which should likely be cos(O1)=0.83 if we are dealing with normal trigonometric values), we can use the Pythagorean identity for sine and cosine, which tells us that sin2(O1) + cos2(O1) = 1. Substituting the known value of the cosine into the equation gives us:

sin2(O1) + (0.83)2 = 1

sin2(O1) + 0.6889 = 1

sin2(O1) = 1 - 0.6889

sin2(O1) = 0.3111

Taking the square root of both sides, and since the angle is in Quadrant I, where sine is positive, we have:

sin(O1) = √(0.3111)

sin(O1) = √(3111/10000)

sin(O1) = √(3111)/100

sin(O1) = 55.7774/100

sin(O1) = 0.557774

Looking at the given options, the exact value of sin(O1) would be closest to 555/1000 which simplifies to 0.555. Therefore, the correct answer is b) sin(O1)=555.