How do you use fundamental identities to find the values of the trigonometric values given tan(t) = -2.87 and csc(t) < 0?

1 Answer
Nov 19, 2016

Answer:

#sint=-0.95#, #cost=0.33#, #tant=-2.87#

#cott=-0.35#, #sect=3.04# and #csct=-1.05#

Explanation:

As #tan(t)=-2.87# and #csc(t) < 0# means both are negative they lie in fourth quadrant. Hence, while #sint# and #cott# will be negative and #cost# and #sect# will be positive. Using these, we calculate all trigonometric ratios (rounding up to two places of decimals).

As #tant=-2.87#, #cott=1/-2.87=-0.35# and

#sec^2t=1+2.87^2=1+8.2369=9.2369#

hence, #sect=sqrt9.2369=3.04# and #cost=0.33#

and #sint=-tantxxcost=-2.87xx0.33=-0.95#

and #csct=1/-0.95=-1.05#

Hence, #sint=-0.95#, #cost=0.33#, #tant=-2.87#

#cott=-0.35#, #sect=3.04# and #csct=-1.05#