Question

Find sin(θ) given that cos(θ) = 1/5, and θ is in quadrant IV.

a) -√24/25
b) √24/25
c) -1/5
d) 1/5

Answer 1

To find sin(theta) given cos(theta) = 1/5 and theta is in quadrant IV, we can use the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 to solve for sin(theta). The answer is -√24/25.

Step-by-step explanation:

To find the value of sin(theta), we can use the relationship between sine and cosine in the fourth quadrant. Since cos(theta) is given as 1/5, we can use the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 to solve for sin(theta). Plugging in the value of cos(theta), we get sin^2(theta) + (1/5)^2 = 1. Solving for sin(theta), we find that sin(theta) = -sqrt(24)/25. Therefore, the answer is option (a) -√24/25.

Answer 2

To solve for sin(θ) with cos(θ) = 1/5 in quadrant IV, we use the Pythagorean identity. Since θ is in the fourth quadrant where sine is negative, the answer is -√24/25.

Step-by-step explanation:

To find sin(θ) given that cos(θ) = 1/5, and θ is in quadrant IV, we can use the Pythagorean identity which states that sin2(θ) + cos2(θ) = 1. Since cos(θ) is known, we can find sin(θ) as follows:

• cos2(θ) = (1/5)2 = 1/25
• sin2(θ) = 1 - cos2(θ) = 1 - 1/25 = 24/25
• Since θ is in the fourth quadrant, sin(θ) is negative, therefore sin(θ) = -sqrt(24/25)

The correct answer is -√24/25, which corresponds to option (a).