How do you evaluate sec(5π12)?

2 Answers
Apr 4, 2016

223

Explanation:

sec = 1/cos . Evaluate cos ((5pi)/12)
Trig unit circle, and property of complementary arcs give -->
cos(5π12)=cos(6π12π12)=cos(π2π12)=sin(π12)
Find sin (pi/12) by using trig identity:
cos2a=12sin2a
cos(π6)=32=12sin2(π12)
2sin2(π12)=132=232
sin2(π12)=234
sin(π12)=232 --> sin(π12) is positive.
Finally,
sec(5π12)=223

You can check the answer by using a calculator.

Apr 4, 2016

sec(5π12)=6+2

Explanation:

secx=1cosx

sec(5π12)=1cos(5π12)

5π12=π4+π6-> Break up into composite Argument

=1cos(π4+π6)

->use cos(A+B)=cosAcosBsinAsinB

=1cos(π4)cos(π6)sin(π4)sin(π6)

=1(22)(32)(22)(12)

=16424=1624=462

=4626+26+2

=4(6+2)62=4(6+2)4

=6+2