Final answer:
To find tanA given sinA=1/3 and A terminates in the first quadrant, we use the Pythagorean identity to find cosA and then divide sinA by cosA to get tanA. The answer is tanA = 1/(√2).
Step-by-step explanation:
To find the value of tanA when sinA = 1/3 and A terminates in the first quadrant, we use the Pythagorean identity for trigonometric functions, which states that sin2A + cos2A = 1. Knowing sinA, we can solve for cosA:
- sin2A = (1/3)2 = 1/9
- cos2A = 1 - sin2A = 1 - 1/9 = 8/9
- cosA = √(8/9), and since A is in the first quadrant where cosine is positive, cosA = √8/3
Now, tanA is the ratio of sinA to cosA. Therefore:
- tanA = sinA / cosA = (1/3) / (√8/3) = √8/8 = 1/(√2)
So, tanA = 1/(√2), which is the answer to the student's question.