It’s your turn on trigonometry by the unit circle

Do your best in trying to solve the following problems.

In any case some of them are solved in the video and all of them are solved in the pdf file below. Also, it may be useful to know the values of the sine and cosine at (pi/6, pi/4, pi/3) (see step 2.11): (sin (pi/6)=1/2, sin (pi/4)=sqrt2/2, sin (pi/3)=sqrt3/2) (cos (pi/6)=sqrt 3/2, cos (pi/4)=sqrt2/2, cos(pi/3)=1/2) Also. recall that (sin(pi+t)=-sin t, ,cos(pi+t)=-cos t) (sin (pi-t)=sin t,, cos(pi-t)=-cos t) (check these identities on the trigonometric circle. Guess the values of (sin(pi/2-t)) and of (cos(pi/2-t) )

Exercise 1.

Compute (cos dfrac {2pi}3), (tanleft(-dfrac pi 3right)) and (sindfrac{19pi}4).

Exercise 2.

Compute the following values: [1) sin dfrac 76pi, cos dfrac {17}6pi, tan dfrac 76pi;] [2) sin dfrac 53pi, cos dfrac {11}3pi, tan dfrac 53pi;] [3) cosleft(- dfrac 76piright), cosleft(- dfrac pi6right), sinleft(- dfrac {2pi}3right). ]