91Ó°ÊÓ

Show you the relationship among \(x, y,\) and \(t\) in parametric functions. For each problem, a. Make a table of \(x\) - and \(y\) -values for a range of \(t\) -values. Include negative values of \(t\) b. Plot the points \((x, y)\) on graph paper and connect them with a line or smooth curve. c. Confirm that your graph is correct by plotting it on your grapher using parametric mode. $$\begin{aligned} &x=3 t+1\\\ &y=2 t-1 \end{aligned}$$

What is the reciprocal property for sec \(x ?\)

Show the steps in trans forming the expression on the left to the one on the right. $$\cos x \tan x \quad \text { to } \quad \sin x$$

If you enter \(\cos ^{2} 0.7\) and \(\sin ^{2} 0.7\) into your calculator, you get these numbers: $$ \begin{array}{l} \cos ^{2} 0.7=0.5849835715 \\ \sin ^{2} 0.7=0.4150164285 \end{array} $$ Without using your calculator, do the addition. What do you notice?

Show you the relationship among \(x, y,\) and \(t\) in parametric functions. For each problem, a. Make a table of \(x\) - and \(y\) -values for a range of \(t\) -values. Include negative values of \(t\) b. Plot the points \((x, y)\) on graph paper and connect them with a line or smooth curve. c. Confirm that your graph is correct by plotting it on your grapher using parametric mode. $$\begin{aligned} &x=1+t^{2}\\\ &y=t+2 \end{aligned}$$

Explain why \(\cot x \cdot \tan x=1\)

a. Plot the graph on your grapher. Sketch the results. b. Use the Pythagorean property for cosine and sine to eliminate the parameter \(t\) c. Explain how you know that the graph is an ellipse or a circle. $$\begin{aligned} &x=3 \cos t\\\ &y=5 \sin t \end{aligned}$$

Write \(\tan x\) in terms of \(\sin x\) and \(\cos x\)

Show the steps in trans forming the expression on the left to the one on the right. $$\csc B \tan B \cos B \quad \text { to } \quad 1$$

a. Plot the graph on your grapher. Sketch the results. b. Use the Pythagorean property for cosine and sine to eliminate the parameter \(t\) c. Explain how you know that the graph is an ellipse or a circle. $$\begin{array}{l} x=6 \cos t \\ y=6 \sin t \end{array}$$