Write the ?rst expression in terms of the second if the terminal point determined by t is in the given quadrant.

Question

  Write the ?rst expression in terms of the second if the terminal point determined by t is in the given quadrant.

1.   sin t, cos t; Quadrant II

 

 Find the values of the trigonometric functions of t from the given information

 

 

2. sin t=3/5,   terminal point of t is in Quadrant II

Answer 1

Hi Dija,

 

For first question, take a look at "UNIT CIRCLE."  You will see that all sin values are "+" and cos values are "-" in 2nd Quadrant.  (90 < θ < 180)

 

sin t = y, cos t = x  -->   ( -x , y ) where  x is defined (-1 < x < 0) and y is defined (0 < y < 1).

 

sin = (y/r), cos = (-x/r), tan = (y/-x), csc = (r/y), sec = (r/-x), cot = (-x/y)

 

 

 

Since sin t = y, you can rewrite as y = (3/5).  If you remember this (sin² + cos² = 1), you can replace sin value into this formula and figure out the x-point.  (3/5)² + (x)² = 1.  You will get x = +(4/5) & -(4/5) and you must choose correct value for 2nd Quadrant where x is (-) which means x = -(4/5).  In conclusion, (-4/5, 3/5) will be the point.

 

I hope you understand how I solved it.

 

Yohan Chu   (LV  NV)

Answer 2

Quadrant II contains pi/2<t<pi values. sin t will give positive y values from a maximum of just under 1 to just above 0 in quadrant II. cos t will give negative x values from a minimum just above 0 to just below -1. 

 

Thus sin t = cos(t-pi/2)

 

as subtracting pi/2 moves t-pi/2 to the first quadrant where cos behaves as sin does.

 

For question 2, cos t can be found by (sin t)^2 + (cos t)^2 = 1, or cos t = 0.8 or 4/5 and tan t = (3/5)/(4/5) or 3/4.