Trigonometry I Trivia Quiz

Answer: 7pi/12

First we must convert 75 degrees to radians. To do this, me must multiply 75 by pi/180. This equals 75pi/180, which simplifies to 5pi/12. Remember that supplementary angles add up to 180 degrees, which is equal to pi in radians. So, to find the supplement of 5pi/12, we must subtract it from pi. pi-5pi/12=7pi/12 (Note: we can also find the supplement of 75 degrees in degrees, and then convert that to radians, for the answer would remain the same).

Answer: x=210 degrees, x=330 degrees

Since csc x=-2, sin x=-1/2. The 2 angles where this occurs is 210 degrees and 330 degrees.

Answer: -N

Remember that the sine function is odd, so sin(-x)=-sin(x). So sin(-53 degrees)=-sin(53 degrees)=-N.

Answer: II

Cosine is negative in quadrants II and III. For tan to also be negative, sin must be positive. Sin is positive in quadrant II.

Answer: 26

csc(26 degrees)=1/sin(26 degrees). Since 1/sin(26 degrees)=1/cos(2x+12 degrees), sin(26 degrees)=cos(2x+12 degrees). Now, please recall that sinx=cos(90 degrees-x). So sin(26 degrees)=cos(90degrees-26 degrees)=cos(64 degrees) So cos(64 degrees)=cos(2x+12 degrees), 64=2x+12, 2x=52, and x=26.

Note that sin(x)=-cos(90+x) as well, so from this relationship we can get x=-38. However, the question asks for a positive value. This adjustment was made so as to eliminate any ambiguity, which I previously had. Thanks to Pilobolus for noticing this.