Answer:
To find the cosine and tangent of β, we can use the trigonometric identity:
sin² β + cos² β = 1
Given that sin β = 0.27, we can substitute this value into the identity:
(0.27)² + cos² β = 1
Simplifying the equation:
0.0729 + cos² β = 1
cos² β = 1 - 0.0729
cos² β = 0.9271
Taking the square root of both sides:
cos β ≈ ± √0.9271
Since β is an acute angle, the cosine function is positive in the first quadrant. Therefore, we take the positive value:
cos β ≈ √0.9271
cos β ≈ 0.9621
To find the tangent of β, we can use the trigonometric identity:
tan β = sin β / cos β
Substituting the given values:
tan β = 0.27 / 0.9621
Calculating the value:
tan β ≈ 0.2809
Therefore, the cosine of β is approximately 0.9621 and the tangent of β is approximately 0.2809.