Asked by Brianna
Find exact value of the expression.
sin( 27pi/4 + 17pi/6)
sin( 27pi/4 + 17pi/6)
Answers
Answered by
Reiny
sin( 27pi/4 + 17pi/6)
= sin(1215° + 510°) --- sometimes I think better with degrees
= sin(1725°)
= sin(285°) ---- 1725 = 4*360 + 285
= - sin 75°
=- sin(45°+30°)
= - [sin45cos30 + cos45sin30]
= - [ (1/√2)(√3/2) + (1/√2)(1/2)]
= - (√3 + 1)/(2√2)
or after rationalizing ...
= -(√6 + √2)/4
= sin(1215° + 510°) --- sometimes I think better with degrees
= sin(1725°)
= sin(285°) ---- 1725 = 4*360 + 285
= - sin 75°
=- sin(45°+30°)
= - [sin45cos30 + cos45sin30]
= - [ (1/√2)(√3/2) + (1/√2)(1/2)]
= - (√3 + 1)/(2√2)
or after rationalizing ...
= -(√6 + √2)/4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.