Question

Suppose zero is an angle in the standard position who’s terminal side is in quadrant IV and cot zero equals -2/17. Find the exact values of the five remaining trigonometric functions of zero

Answer 1

SOLUTIONS

Find the exact values of the five remaining trigonometric functions of zero:

$cot\theta=-\frac{2}{17}$

Suppose theta is an angle in the standard position

Cot = adj/opp

$\begin{gathered} adj=17 \\ opp=-2 \end{gathered}$

Pythagoras theorem

$\begin{gathered} hyp^2=opp^2+adj^2 \\ x^2=(-2)^2+17^2 \\ x^2=4+289 \\ x^2=293 \\ x=\sqrt{293} \end{gathered}$

Hypotenuse = sqrt293

Opposite = -2

Adjacent = 17

$\begin{gathered} sin\theta=-\frac{2}{\sqrt{293}},cos\theta=\frac{17}{\sqrt{293}},cosec\theta=-\frac{\sqrt{293}}{2} \\ sec\theta=\frac{\sqrt{293}}{17},tan\theta=-\frac{17}{2} \end{gathered}$

correct answer = Option A