Question

If sin(x) = 1/2, what is cos(x) and tan(x)? Explain in full sentences

Answer 1

When sin(x) = 1/2, assuming x is in the first quadrant, cos(x) can be found using the Pythagorean theorem, resulting in cos(x) = √(3)/2. The tangent, tan(x), can be calculated as sin(x)/cos(x), which simplifies to tan(x) = √(3)/3.

Step-by-step explanation:

Given that sin(x) = 1/2 and assuming x is in the first quadrant, we can determine the values of cos(x) and tan(x) using the Pythagorean identity.

For any angle x in a right triangle, the Pythagorean theorem tells us that:

• sin2(x) + cos2(x) = 1

Since we know sin(x) is 1/2, we can find cos(x) by rearranging the identity:

• cos2(x) = 1 - sin2(x)
• cos2(x) = 1 - (1/2)2
• cos2(x) = 1 - 1/4
• cos2(x) = 3/4
• cos(x) = ±√(3/4)

Since we are assuming x is in the first quadrant where cosine values are positive, cos(x) = √(3)/2. To find tan(x), we use the definition tan(x) = sin(x)/cos(x):

• tan(x) = (1/2) / (√(3)/2)
• tan(x) = 1/√(3)
• tan(x) = √(3)/3 (after rationalizing the denominator)

Thus, cos(x) equals √(3)/2 and tan(x) equals √(3)/3 assuming the angle x is in the first quadrant where both sine and cosine are positive.

Answer 2

In quadrant #1:
When sin (x) = 1/2
cos(x) = sqrt(3)/2
Tan(x) = sqrt(3)/3
In quadrant #2:
Cos -
Sin +
Tan -