Question

If sin 46=a determine the following in terms of
cos 46=(opp )/(adj )

Answer 1

To find cos 46° in terms of the opposite over adjacent, we use the Pythagorean identity, resulting in cos 46° = √(1 - a²), assuming the angle is in the first quadrant.

Step-by-step explanation:

If sin 46° = a, we are asked to determine cos 46° in terms of (opp)/(adj), which represents the ratio of the opposite side to the adjacent side in a right triangle. Since sin 46° is equal to a and by the Pythagorean identity: sin² θ + cos² θ = 1, we can find cos 46° by rearranging the identity as cos² θ = 1 - sin² θ.

Therefore, we get cos 46° = √(1 - a²). This is under the assumption that 46° is in the first quadrant where cosine is positive. If 46° were in the second quadrant, we would take the negative square root.