Final answer:
To find sin 2x, cos 2x, and tan 2x given sin x = 1/√10 and x terminates in quadrant I, we can use the double angle identities. Substituting the given value, sin 2x = 2√10 / 11, cos 2x = 99/110, and tan 2x = 2/3.
Step-by-step explanation:
We are given that sin x = 1/√10 and x terminates in quadrant I. To find sin 2x, cos 2x, and tan 2x, we can use the double angle identities.
1. sin 2x = 2sin x cos x
2. cos 2x = cos² x - sin² x
3. tan 2x = (2tan x) / (1 - tan² x)
Substituting sin x = 1/√10, we can calculate the values of sin 2x, cos 2x, and tan 2x using the above identities.
sin 2x = 2(1/√10)√(10/11) = 2√10 / 11
cos 2x = (√(10/11))² - (1/√10)² = 10/11 - 1/10 = 99/110
tan 2x = (2(1/√10)) / (1 - (1/√10)²) = (2/√10) / (1 - 1/10) = 2/√10 * 10/9 = 2/3