If sinB=3/4 and the terminal side of the angle is in quadrant II, how do you find the other five trigonometric functions of B?

1 Answer
Alan P.
Oct 7, 2015

#color(white)("XXXXXXXXXXXXXXXXXXXX")sec(B)4/3#
#cos(B)=-sqrt(7)/4color(white)("XXXXXXXXXX")sec(B)=4/sqrt(7)=(4sqrt(7))/7#
#tan(B)=-3/sqrt(7)=-(3sqrt(7))/7color(white)("XXXX")cot(B)=-sqrt(7)/3#

Explanation:

Setting the hypotenuse to #4# units
If #sin(B)=3/4# and #B# is in Q II
the opposite side (#y#) is #3#
and
the adjacent side (#x#) is #-sqrt(7)# (by Pythagorean Theorem)

All trigonometric functions of #B# follow directly from this.

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