SOLUTION: Determine the exact value of each of the following and what quadrant they are in, a) tan(-210 degrees) b) Sin 300 degrees

Algebra ->  Trigonometry-basics -> SOLUTION: Determine the exact value of each of the following and what quadrant they are in, a) tan(-210 degrees) b) Sin 300 degrees      Log On


   

Question 1165906: Determine the exact value of each of the following and what quadrant they are in,
a) tan(-210 degrees)
b) Sin 300 degrees
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
----------------
Sin 300 degrees
----------------

Refer to Unit Circle.
See that 300 degrees is 60 degrees less than 360 degrees. This is like +60 degrees, but the sign is negative. Instead of sqrt%283%29%2F2 for sine, it is -sqrt%283%29%2F2; and is in quadrant 4.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a)
tan%28-210%29
Use the following property :
tan%28-x%29=-tan+%28x%29
tan%28-210%29=-tan%28210%29
tan%28210%29=tan%28180%29%2Btan%2830%29 ....since tan%28180%29=0
tan%28210%29=tan%2830%29
tan%2830%29=-1%2Fsqrt%283%29
=> tan%28-210%29=-1%2Fsqrt%283%29

b)
sin%28300%29 degrees
Use the following property :
sin%28x%29=cos%2890-x%29
=> sin%28300%29=cos%2890-300%29=> sin%28300%29=cos%28-210%29
then cos%28-210%29=-cos%28210%29
and -cos%28210%29=-cos%28180%2B30%29+
Using the summation identity :
cos%28x%2B+y+%29=+cos+%28x+%29+cos+%28y+%29-+sin+%28x+%29+sin+%28y+%29
cos%28180%2B+30+%29=+cos+%28180+%29+cos+%2830+%29-+sin+%28180+%29+sin+%2830+%29
since
cos%28180%29=-1
cos%2830%29=sqrt%283%29%2F2
sin+%28180+%29=0
sin+%2830+%29=1%2F2
we have
cos%28180%2B+30+%29=+%28-1%29%28sqrt%283%29%2F2%29-+0%2A%281%2F2%29
cos%28180%2B+30+%29=+-sqrt%283%29%2F2%29
=>sin%28300%29=+-sqrt%283%29%2F2%29