# trig question cot, csc?

Find the exact value of the problem, no decimal form.

{1/[cot(pi/4)]} - {2/[csc(pi/6)]}

please help me, it looks confusing but its, (1 over cotangent of pi/4) minus (2 over cosecant of pi/6)

Thanks

Relevance
• Puggy
Lv 7

Keep in mind that pi/4 and pi/6 are two familiar values on the unit circle. We know the sine and cosine of them, so all we have to do is convert everything to sine and cosine. cot(x) = cos(x)/sin(x), and csc(x) = 1/sin(x)

[1/cot(pi/4)] - [2/csc(pi/6)]

[1/(cos(pi/4)/sin(pi/4)] - [2/(1/sin(pi/6))]

Now, we have complex fractions, which we can make into simple fractions. I won't show the details, but the above should simplify into

sin(pi/4)/cos(pi/4) - 2sin(pi/6)

Now, we solve as normal.

[sqrt(2)/2] / [sqrt(2)/2] - 2(1/2)

1 - 1 = 0

Well you should know that 1/cot a = tan a & 1/sin a = cosec a

then the question can be put in the form,

[1/cot (pi/4)] -2[1/cosec (pi/6)]

= tan (pi/4) -2.sin (pi/6)

= 1 -2(1/2)

= 0

tan (pi/4) = 1 and sin (pi/6) = 1/2 , can be taken as standard values and verified by constructing right angled triangles.

hope this helps!

• 3 years ago

Csc Pi Over 6

what is confusing you?

your exp= tan pi/4 - 2*sin pi/6

= 1- 2(.5) = 0

{1/[cot(π/4)]} - {2/[csc(π/6)]}

= tan(π/4) - 2sin(π/6)

= 1 - 2(1/2) = 1 - 1 = 0

A little more familiarity with your trig functions will help you a lot. These are very common angles and the student is expected to know, or be able to quickly calculate, the exact values of trig functions of the angles 0, π/6, π/4, π/3, π/2, π, and multiples thereof.

Also, if you are unsure of the values of tan, cot, csc, and sec, convert them to sin and cos first. Then calculate.

[1/(cos(pi/4)/sin(pi/4))]-[2/(1/sin(pi/6))]=

[sin(pi/4)/cos(pi/4)]-[(2sin(pi/6)]=

tan(pi/4)-2sin(pi/6)

use the trig exact value table remember tan 45(Pi/4)=1 and sin 30(Pi/6)=sqrt(3)/2

=1-2(sqrt(3)/2)

=1-sqrt(3) or approximately equals

= - 0.732050808 to 9 decimal places