Math destroyer Test 11 #6

[qkrgkssk]

Need help with problem number 6 of Test 11.
Find the value of cos(-3pi/4)x(tan 7pi/6).
Thank you for your help.

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[DAT Destroyer]

Need help with problem number 6 of Test 11.
Find the value of cos(-3pi/4)x(tan 7pi/6).
Thank you for your help.

First you need to know that cos(-x) = cos(x). Cos(-3π/4) = cos(3π/4). 3π/4 is in the second quadrant and hence cos(3π/4) is negative. The reference angle is π/4. Therefore cos(3π/4)= -√2/2
7π/6 is in the third quadrant and tan(7π/6) is positive. The reference angle is π/6 and tan(7π/6)=√3/3
Multiply both quantities to get -√6/6.