Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Expert Q&A
Geometry
Trigonometry
1 - 15 of 5K+ results
geometry

Consider the following two sets of parametric equations:

Line   1:  x=1−t,  y=3t,  z=−6+5t,Line   2:  x=−1+2t,  y=6−6t,  z=4−10t.\begin{align*} \text{Line\; 1:}&\; x =1 - t,\; y= 3t,\; z = -6 + 5t,\\ \text{Line\; 2:}&\; x = -1 + 2t,\; y = 6 - 6t,\; z = 4 - 10t. \end{align*}

a) Find two points that lie on Line 1 by setting t=0t = 0 and t=1t = 1 in its parametric equations. Then show that these points also lie on Line 2 by finding two values of the parameter that give these points when substituted into the parametric equations for Line 2.

b) Show that the following two lines are not the same by finding a point on Line 3 and then showing that it does not lie on Line 4.

Line   3:  x=4t,  y=3−6t,  z=−5+2t,Line   4:  x=8−2t,y=−9+3t,z=6−t.\begin{align*} \text{Line\; 3:}&\; x= 4t,\; y= 3 - 6t,\; z = -5 + 2t,\\ \text{Line\; 4:}&\; x = 8 - 2t, y = -9 + 3t, z = 6 - t. \end{align*}

Verified answer
trigonometry

If sin t=7/12 find cos(π/2 − t).

Verified answer