Suppose sin(4) -
Use the trig identity sin² (A) + cos2 (4) - 1 to find cos(4) in quadrant I. Show all steps and round to ten-thousandth.
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Suppose sin(4) - Use the trig identity sin² (A) + - 1
To find cos(4) using the trig identity sin^2(A) + cos^2(A) = 1, we can rearrange the formula as:
cos^2(4) = 1 - sin^2(4)
Now, let's substitute the given value of sin(4) into the equation:
cos^2(4) = 1 - (0.325)^2
cos^2(4) = 1 - 0.105625
cos^2(4) = 0.894375
To find cos(4), we take the square root of both sides:
cos(4) = ± √0.894375
Since we are looking for the value of cos(4) in quadrant I, where cos is positive, we can discard the negative sign:
cos(4) = √0.894375
cos(4) ≈ 0.9461 (rounded to ten thousandth)
To find cos(4) using the trig identity sin²(A) + cos²(A) = 1, we need to have the value of sin(4).
Given that sin(4) = -0.7568, we can use the identity to obtain:
sin²(4) + cos²(4) = 1
(-0.7568)² + cos²(4) = 1
0.57276544 + cos²(4) = 1
Now, we can solve for cos²(4):
cos²(4) = 1 - 0.57276544
cos²(4) = 0.42723456
Next, we can take the square root of both sides to find cos(4):
cos(4) = ±√(0.42723456)
cos(4) = ±0.6547 (rounded to four decimal places)
Since we are looking for the value of cos(4) in quadrant I, the angle is positive:
cos(4) = 0.6547 (rounded to four decimal places) in quadrant I.