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

`\sin O \approx 0.919`,
`\sec O \approx -2.539` and
`\tan O = -(7)/(3)`.

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 = (1)/(\cos O) = \frac{\sqrt{x^(2)+y^(2)}}{x}`

`\tan O = (\sin O)/(\cos O) = (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 = (7)/(-3)`

`\tan O = -(7)/(3)`