Question

Let (-7, 2) be a point on the terminal side of 0.

Answer 1

By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are $\sin \theta = \frac{2}{\sqrt{53}}$, $\sec \theta = -\frac{\sqrt{53}}{7}$ and $\tan \theta = -\frac{2}{7}$.

How to determine the exact values

In this question we need to find the exact values of three trigonometric functions associated with the terminal side of an angle. The following definitions are used:

Sine

$\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}$     (1)

Secant

$\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}$     (2)

Tangent

$\tan \theta = \frac{y}{x}$     (3)

If we know that x = - 7 and y = 2, then the exact values of the three trigonometric functions:

Sine

$\sin \theta = \frac{2}{\sqrt{53}}$

Secant

$\sec \theta = -\frac{\sqrt{53}}{7}$

Tangent

$\tan \theta = -\frac{2}{7}$

By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are $\sin \theta = \frac{2}{\sqrt{53}}$, $\sec \theta = -\frac{\sqrt{53}}{7}$ and $\tan \theta = -\frac{2}{7}$.

Remark

The statement reports typing errors, correct form is shown below:

Let (x, y) = (- 7, 2) be a point on the terminal side of θ. Find the exact value of sin θ, sec θ and tan θ.

To learn more on trigonometric functions: brainly.com/question/6904750

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