Use the fact that sin38°≈0.6157 to answer this question.
cos[BLANK] °≈0.6157
what rubbish. all that work, and you did not even answer the question!
since sinx = cos(90-x), if sin38°≈0.6157 then cos52°≈0.6157
You are correct, I apologize for the mistake in my previous response. Since sin x = cos(90 - x), if sin 38° ≈ 0.6157, then cos 52° ≈ 0.6157. Thank you for pointing that out.
To find the angle that has a cosine value of approximately 0.6157, we can use the fact that the cosine of an angle is equal to the sine of its complement.
Let's call the unknown angle x. According to the given fact, sin(38°) ≈ 0.6157.
Since cos(x) = sin(90° - x), we can write:
cos(x) ≈ sin(90° - x)
Given that sin(38°) ≈ 0.6157, we can substitute it into the equation:
cos(x) ≈ 0.6157
Now we solve for x by taking the inverse cosine on both sides:
x ≈ cos^(-1)(0.6157)
Using a calculator or table of trigonometric values, we find that the inverse cosine of 0.6157 is approximately 51.36°.
Therefore, cos[BLANK] ° ≈ 0.6157 can be replaced with cos(51.36°) ≈ 0.6157.
To find the value of the missing angle, we can use the identity:
cos^2θ + sin^2θ = 1
Since we know sin38°≈0.6157, we can substitute this value in the equation above:
cos^2θ + (0.6157)^2 = 1
cos^2θ + 0.37950649 = 1
cos^2θ = 1 - 0.37950649
cos^2θ ≈ 0.62049351
To find the value of cosθ, we take the square root of both sides:
cosθ ≈ √0.62049351
Using a calculator, we find:
cosθ ≈ 0.7875
Therefore, cosθ≈0.7875.