what is the exact value(using unit circle):
sin(9pi/2)
cos(7pi/6)
tan(-5pi/6)
csc(26pi/3)
sec(-5pi/2)
cot(13pi/2)
identify sin x cos x and tan x:
cos x=-√2/6, in quadrant 2
tan x=-√3, six x>0
Here are some hintsthis is the same as $\displaystyle \pm \sin \frac {\pi}2$
this is the same as $\displaystyle \pm \cos \frac {\pi}6$cos(7pi/6)
this is the same as $\displaystyle \pm \tan \frac {\pi}6$tan(-5pi/6)
this is the same as $\displaystyle \pm \csc \frac {\pi}3$csc(26pi/3)
this is the same as $\displaystyle \pm \sec \frac {\pi}2$sec(-5pi/2)
this is the same as $\displaystyle \pm \cot \frac {\pi}2$cot(13pi/2)
for all of the above, you should know the values of the trig functions evaluated at those special angles. to decide whether they are positive or negative, figure out what quadrant the original angles are in, and that will tell you. remember, all trig ratios are positive in the first quadrant, only sine and cosecant are positive in the second, only tangent and cotangent are positive in the third, and only cosine and secant are positive in the fourth.
Hint: recall that $\displaystyle \sin^2 x + \cos^2 x = 1$identify sin x cos x and tan x:
cos x=-√2/6, in quadrant 2
tan x=-√3, six x>0
and that $\displaystyle \tan x = \frac {\sin x}{\cos x}$
again, pay attention to what signs your trig ratios should be depending on what quadrant your angle is in