Question

suppose cos(A)=0.325 use trig identity sin^2(A)+cos^2(A)=1 and tan(A)=sin(A)/cos(A) to find tan(A) in quadrant IV

Answer 1

In quadrant IV, cosine is positive, and sine is negative. Given that cos(A) = 0.325, you can use the trig identity sin^2(A) + cos^2(A) = 1 to find sine (sin(A)) in quadrant IV:

sin^2(A) + cos^2(A) = 1

sin^2(A) + 0.325^2 = 1

sin^2(A) + 0.105625 = 1

sin^2(A) = 1 - 0.105625

sin^2(A) = 0.894375

Now, take the square root to find sin(A):

sin(A) = √0.894375 ≈ 0.9453 (rounded to four decimal places)

Now, you can find tan(A) using the tangent identity:

tan(A) = sin(A) / cos(A)

tan(A) = 0.9453 / 0.325 ≈ 2.9062 (rounded to four decimal places)

So, in quadrant IV, tan(A) is approximately 2.9062.