Question

Suppose sin(A) = 2/5. Use the trig identity sin^2(A) + cos^2(A) = 1 to find cos(A) in quadrant I. Round to ten-thousandth.

a) 0.9366
b) 0.7810
c) 0.3432
d) 0.5321

Answer 1

Using the trigonometric identity sin^2(A) + cos^2(A) = 1 and knowing sin(A) = 2/5, we solve for cos(A) in quadrant I to find that cos(A) = 0.9366 when rounded to four decimal places.

Step-by-step explanation:

To find cos(A) when sin(A) = 2/5 and A is in quadrant I, we use the trigonometric identity sin²(A) + cos²(A) = 1. Squaring the given sin(A) value gives us sin²(A) = (2/5)² = 4/25. To find cos²(A), we rearrange the identity:

cos²(A) = 1 - sin²(A) = 1 - 4/25 = 21/25.

Since we're looking for cos(A) and A is in the first quadrant, where cosine is positive, we take the positive square root:

cos(A) = √(21/25) = √21 / 5.

Rounded to four decimal places, cos(A) = 0.9366.

Thus, the correct answer is (a) 0.9366.