SOLUTION: Use the CAST rule to state the sign of each value. Check using calculator. (a) tan 15 degrees (b) sin 120 degrees (c)cos 135 degrees (d) tan(-15 degrees) (e) sin(-45 degrees

Algebra ->  Trigonometry-basics -> SOLUTION: Use the CAST rule to state the sign of each value. Check using calculator. (a) tan 15 degrees (b) sin 120 degrees (c)cos 135 degrees (d) tan(-15 degrees) (e) sin(-45 degrees      Log On


   



Question 933382: Use the CAST rule to state the sign of each value. Check using calculator.
(a) tan 15 degrees
(b) sin 120 degrees
(c)cos 135 degrees
(d) tan(-15 degrees)
(e) sin(-45 degrees)
Thank you

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
here is a pattern:
In the first quadrant (I), all ratios are positive.

In Quadrant II, sin%28theta%29 is positive, cos%28theta%29 and tan+%28theta%29 are negative.
In Quadrant III, tan+%28theta%29 is positive (both x and y are negative, so ​x%26%238203%3B%26%238203%3By%26%238203%3B%26%238203%3B is positive), sin%28theta%29 and cos+%28theta%29 are negative.
In Quadrant IV, cos%28theta%29 is positive, sin%28theta%29 and tan%28theta%29 are negative.


Of course the reciprocal ratios, csc+%28theta%29, sec%28theta%29 and cot%28theta%29 follow the same pattern:
In Quadrant II, csc%28theta%29 is positive, sec%28theta%29 and cot%28theta%29 are negative.
In Quadrant III, cot%28theta%29 is positive, csc%28theta%29 and sec%28theta%29 are negative.
In Quadrant IV, sec%28theta%29 is positive, csc%28theta%29 and cot%28theta%29 are negative.


then, your answers will be:


(a) tan%2815%29 degrees ->In the first quadrant (I), all ratios are positive.
(a) tan%2815%29=2-sqrt%283%29=0.268
(b) sin%28120%29 degrees ->In Quadrant II sin%28theta%29 is positive
sin%28120%29=sqrt%283%29%2F2=0.866
(c)cos%28135%29 degrees->In Quadrant II+cos%28theta%29 is negative
cos%28135%29=-1%2Fsqrt%282%29=-0.707
(d) tan%28-15%29 degrees -> In Quadrant IV tan%28theta%29 is negative
tan%28-15%29=sqrt%283%29-2=-0.268
(e) sin%28-45%29 degrees ->In Quadrant IV sin%28theta%29 is negative
sin%28-45%29=-1%2Fsqrt%282%29=-0.707