SOLUTION: Is this right? please check exact value of tan(5π/3)sec(-5π/6) and other? Find the exact value of: tan(5π/3)sec(-5π/6) sin(27π/4)cos(1043π)

Algebra ->  Trigonometry-basics -> SOLUTION: Is this right? please check exact value of tan(5π/3)sec(-5π/6) and other? Find the exact value of: tan(5π/3)sec(-5π/6) sin(27π/4)cos(1043π)      Log On


   

Question 923299: Is this right? please check exact value of tan(5π/3)sec(-5π/6) and other?
Find the exact value of:
tan(5π/3)sec(-5π/6)
sin(27π/4)cos(1043π)

I think is I must find must the coterminal point then use trig identity to solve. therefore
5π/3+2π/1 = 11π/3
tan = x/y but 11π/3 I dont see with my unit circle? so not sure
sec(-5π/6)
-5π/6+2π/1 = 7π/6
sec = 1/x = -2/√(3)

sin(27π/4) I think for this I must subtract 2π and therefore
27π/4-2π/1
27π/4-8π/4
=3π/4
sin =y/r
=(√2/2)
cos(1043π)
I know there is some trick with this but I forget it. I think I have to break up?
Please help
Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Is this right? please check exact value of tan(5π/3)sec(-5π/6) and other?
Find the exact value of:
tan(5π/3)sec(-5π/6)
sin(27π/4)cos(1043π)
I think is I must find must the coterminal point then use trig identity to solve. therefore
5π/3+2π/1 = 11π/3 *********** There's no reason to add 2pi.
----
You can just use a calculator. You might change -5pi/6 to 7pi/6, but it's not necessary with a calculator.
---
tan = x/y but 11π/3 I dont see with my unit circle? so not sure
Don't add 2pi. 5pi/3 is on the unit circle (= 300 degs)
sec(-5π/6)
-5π/6+2π/1 = 7π/6
sec = 1/x = -2/√(3) **** sec = 1/cos, not 1/x, but it is -2/sqrt(3)
---
====================================
sin(27π/4) I think for this I must subtract 2π and therefore
27π/4-2π/1
27π/4-8π/4
=3π/4 (subtracting 2pi twice --> sin(3pi/4)
sin =y/r
=(√2/2)
===================================
cos(1043π)
= cos(521*(2pi) + pi)
= cos(pi)
= -1