math
posted by TEETEE .
Use an Addition or Subtraction Formula to find the exact value of the expression.
Sin(−5π/12)

some students have less difficulty if the angle is in degrees.
Let's try this approach ....
5π/12 radians = 75°
so sin(5π/12)
= sin(75°) which is in quadrant IV, making the sine negative
= sin(75°)
= sin(30° + 45°)
= (sin30cos45 + cos30sin45)
= ( (1/2)(√2/2) + (√3/3)(√2/2) )
=  √2/4  √6/4
so sin(05π/12) = √2/4  √6/4
check:
on my calculator:
sin(5π/12) = .9659...
and √2/4  √6/4 = .9659..
My answer is correct
Respond to this Question
Similar Questions

Math
Evaluate *Note  We have to find the exact value of these. That I know to do. For example sin5π/12 will be broken into sin (π/6) + (π/4) So... sin 5π/12 sin (π/6) + (π/4) sin π/6 cos π/4 + cos … 
Math
Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value. (tan(π/2)+tan((2π)/3)) / (1tan(π/2)tan((2π)/3)) Answer=__________ Exact value … 
Precalculus
Use one of the identities cos(t + 2πk) = cos t or sin(t + 2πk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(19π/4) (b) sin(−19π/4) (c) cos(11π) (d) cos(53π/4) … 
trig
Use an addition or subtraction formula to simplify the expression: tan(2−u)=cot(f(u)). 
PreCalc : 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? 
PreCalculus
Use an Addition or Subtraction Formula to find the exact value of the expression: tan7π/12 
PreCalc
1) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 12° cos 18° − sin 12° sin 18° And Find its exact value. 2) Use an Addition or Subtraction Formula to write the … 
PreCalc
I am really struggling with how to do these problems, I posted them a few minutes ago but the answers/work shown was incorrect. 1) a) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one … 
trigonometry
1) Find the exact value of the expression: tan−1(tan(−120651/47π))... How do you find Tan(120651/47pi)? 
precalc
Find the exact value of each expression, if it exists: the 1 are representing the inverse functions! (a) sin 1 (√2/2) (b) cos−1 (−1) (c) sin( sin−1 (π)) (d) cos−1(cos(−4π/ …