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dourtuntellorvl

dourtuntellorvl

Answered question

2022-06-25

If cos t = 3 / 5, where π < t < 3 π / 2, what is sin ( t / 2 )?

Answer & Explanation

svirajueh

svirajueh

Beginner2022-06-26Added 29 answers

Notice, your mistake sin t 1 2 sin 2 t 2
Use the following formula
cos t = 1 2 sin 2 t 2
sin t 2 = ± 1 cos t 2
sin t 2 = ± 1 ( 3 ) 5 2 = ± 2 5
But, π < t < 3 π 2 π 2 < t 2 < 3 π 4 sin t 2 > 0 hence,
sin t 2 = 2 5
shmilybaby4i

shmilybaby4i

Beginner2022-06-27Added 1 answers

Full angle t is in third quadrant, so sine of half angle in first quadrant
= 1 cos t 2 = + 2 5 5

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