# trig

posted by Brianna

Find exact value of the expression.
sin( 27pi/4 + 17pi/6)

1. 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

## Similar Questions

1. ### MATH

1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL STEPS) sin 2x - sin x = 0 2.) GIVEN: sin u = 3/5, 0 < u < ï/2 Find the exact values of: sin 2u, cos 2u and tan 2u using the double-angle formulas. 3.)Use …
2. ### trig

Given that sin (pi/10)=(sqrt(5)-1)/4, use double-angle formulas to find an exact expression for sin(pi/5).
3. ### trig

Find the exact value. Without using a calculator a) cos (-17pi/6) b) sec (3pi/2)
4. ### trig

find the exact value of the expression , sin-1(-0.5)
5. ### Pre-Calc : Find the Exact Value of the Expression

Find the exact value of the expression without a calculator: sin(3π/4+5π/6) I've done: sin(9π/12 + 10π/12) =sin(19π/12) What do I do now?
6. ### Math

1. Find the exact value of 2tan pi/12 / 1-tan^2 pi/12 root 3/3?
7. ### Trig hep, please? Thank you!

1. Find the exact value of sin(195(degrees)) 2. If cot2(delta)=5/12 with 0(<or =)2(delta)pi, find cos(delta), sin(delta) , tan(delta). 3.find the exact value of sin2(x) if cos(x)= 4/5. (X is in quadrant 1) 4. Find the exact value …