Question

Let (-3, 7) be a point on the terminal side of 0.
Find the exact values of sin 0, sec 0, and tan 0.

Answer 1

Answer:

$\sin O \approx 0.919$, $\sec O \approx -2.539$ and $\tan O = -\frac{7}{3}$.

Step-by-step explanation:

Given a point (x, y) with respect to origin and in rectangular coordinates, the exact value of sine, secant and tangent functions are, respectively:

$\sin O = \frac{y}{\sqrt{x^{2}+y^{2}}}$

$\sec O = \frac{1}{\cos O} = \frac{\sqrt{x^{2}+y^{2}}}{x}$

$\tan O = \frac{\sin O}{\cos O} = \frac{y}{x}$

Given that $x = -3$ and $y = 7$, the exact values of sine, secant and tangent are:

$\sin O = \frac{7}{\sqrt{(-3)^{2}+7^{2}}}$

$\sin O \approx 0.919$

$\sec O = \frac{\sqrt{(-3)^{2}+7^{2}}}{-3}$

$\sec O \approx -2.539$

$\tan O = \frac{7}{-3}$

$\tan O = -\frac{7}{3}$