Final answer:
The tangent of angle A in quadrant IV, where cos(A) = 0.325, is computed using the trigonometric identities. After finding sin(A) by first determining sin²(A), tan(A) is calculated by dividing sin(A) by cos(A) to be approximately -2.9108, which does not match the given options.
Step-by-step explanation:
To find tan(A) using the fact that cos(A) = 0.325 and in quadrant IV, we first use the identity sin²(A) + cos²(A) = 1 to find the sine of A:sin²(A) = 1 - cos²(A) = 1 - (0.325)² = 1 - 0.105625sin²(A) = 0.894375sin(A) = √0.894375 (Since A is in the fourth quadrant, we take the negative square root because sine is negative in the fourth quadrant.)sin(A) = -0.94625 (Round to fifth decimal first before final answer)Now, we use the identity tan(A) = sin(A) / cos(A) to find the tangent:tan(A) = -0.94625 / 0.325tan(A) = -2.910769230tan(A) ≈ -2.9108 (Rounded to the ten-thousandthHowever, the given options do not include this result, which means there may be a mistake.
Please check the options and the calculation again.To find tan(A) in quadrant IV, we can use the trigonometric identity tan(A) = sin(A) / cos(A). Given that cos(A) = 0.325, we can use the Pythagorean identity sin²(A) + cos²(A) = 1 to find sin(A). Rearranging this equation, we have sin²(A) = 1 - cos²(A), and substituting the given value of cos(A), we get sin²(A) = 1 - 0.325² = 0.89375. Taking the square root of both sides, we find that sin(A) ≈ 0.9457.Now, we can substitute the values of sin(A) and cos(A) into the equation tan(A) = sin(A) / cos(A). We have tan(A) ≈ 0.9457 / 0.325 ≈ 2.9138.Therefore, rounding to four decimal places, tan(A) in quadrant IV is approximately 2.9138, which corresponds to answer choice a) 1.3632.