Question 933382
here is a pattern:

In the first quadrant ({{{I}}}), all ratios are {{{positive}}}.


    In Quadrant {{{II}}}, {{{sin(theta)}}} is positive, {{{cos(theta)}}} and {{{tan (theta)}}} are negative.

    In Quadrant {{{III}}}, {{{tan (theta)}}} is positive (both {{{x}}} and {{{y}}} are negative, so ​{{{x​​y​​}}} is positive), {{{sin(theta)}}} and {{{cos (theta)}}} are negative.

    In Quadrant {{{IV}}}, {{{cos(theta)}}} is positive, {{{sin(theta)}}} and {{{tan(theta)}}} are negative.



Of course the reciprocal ratios, {{{csc (theta)}}}, {{{sec(theta)}}} and {{{cot(theta)}}} follow the same pattern:

    In Quadrant {{{II}}}, {{{csc(theta)}}} is positive, {{{sec(theta)}}} and {{{cot(theta)}}} are negative.

    In Quadrant {{{III}}}, {{{cot(theta)}}} is positive, {{{csc(theta)}}} and {{{sec(theta)}}} are negative.

    In Quadrant {{{IV}}}, {{{sec(theta)}}} is positive, {{{csc(theta)}}} and {{{cot(theta)}}} are negative.



then, your answers will be:



(a) {{{tan(15)}}} degrees ->In the first quadrant ({{{I}}}), all ratios are {{{positive}}}.

(a) {{{tan(15)=2-sqrt(3)=0.268}}}

(b) {{{sin(120)}}} degrees ->In Quadrant {{{II}}} {{{sin(theta)}}} is {{{positive}}}

{{{sin(120)=sqrt(3)/2=0.866}}}

(c){{{cos(135)}}} degrees->In Quadrant {{{II}}}{{{ cos(theta)}}}  is {{{negative}}}

{{{cos(135)=-1/sqrt(2)=-0.707}}}

(d) {{{tan(-15)}}} degrees -> In Quadrant {{{IV}}} {{{tan(theta)}}} is {{{negative}}}

{{{tan(-15)=sqrt(3)-2=-0.268}}}

(e) {{{sin(-45)}}} degrees ->In Quadrant {{{IV}}} {{{sin(theta)}}} is {{{negative}}}

{{{sin(-45)=-1/sqrt(2)=-0.707}}}