<p>Ok here is the question:</p>
<p>Suppoise the terminal point (x, y) for an arclength t is on the unit circl in quadrant IV. Suppose x =9/10. Find the exact value of tan t. </p>
<p>This is a question on the trig review in calculus. I can't seem to understand this question. Can anyone please help me?</p>
<p>Um x = sinx, y = cosx</p>
<p>(sinx)^2 + (cosx^2) = 1
so... (9/10)^2 + (cosx)^2 = 1</p>
<p>cosx = sqrt (1-81/100)
x = cos -1 (3/10)</p>
<p>Then just solve for tan once u get the angle.</p>
<p>thanks also.</p>
<p>it is the other way around x being cos and y being sin.</p>
<p>Typically it is referred to as sin = y/r cos = x/r where r is the radius.
tan is obviously sin/cos so y/x. However in this case because it is the unit circle the radius is 1.</p>
<p>the cos^2 +sin^2 = 1 still works however we must use different values.</p>
<p>so (9/10)^2 +sin^2 = 1
81/100 +sin^2 = 1
sin^2 = 19/100
sin = -sqrt(19)/10
sin = aprx. -.436</p>
<p>it is neg because of quadrant 4 making x+ and y-</p>
<p>so tan is (-sqrt(19)/10)/(9/10) which is exact as -sqrt(19)/9 or aprx. -.484</p>
<p>Oh crap, yea you're right. I made a stupid mistake, sorry.</p>