Question

Determine the three reciprocal trigonometric ratios of the angle.

Answer 1

Answer: Option b.

Step-by-step explanation:

The reciprocal trigonometric ratios are:

1) Cosecant ($csc\theta$), which is the reciprocal of the sine.

2) Secant ($sec\theta$), which is the reciprocal of the cosine.

3) Cotangent  ($cot\theta$), which is the reciprocal of the tangent.

If:

$sin\theta=\frac{opposite}{hypotenuse}}\\\\cos\theta=\frac{adjacent}{hypotenuse}\\\\tan\theta=\frac{opposite}{adjacent}$

Then:

$csc\theta=\frac{hypotenuse}{opposite}}\\\\sec\theta=\frac{hypotenuse}{adjacent}\\\\cot\theta=\frac{adjacent}{opposite}$

Knowing that:

$opposite=9\\adjacent=12\\hypotenuse=15$

You can substitute these values into the trigonometric ratios to find the values of the reciprocal ratios of the angle $\theta$:

$csc\theta=\frac{15}{9}}\\\\sec\theta=\frac{15}{12}\\\\cot\theta=\frac{12}{9}$

Answer 2

Answer:

The correct option is:

                  Option: c and option: d

Step-by-step explanation:

We know that with respect to the angle θ, the trigonometric ratios are defined as follows:

$\sin \theta=\dfrac{opposite}{Hypotenuse}\\\\\\\cos \theta=\dfrac{adjacent}{Hypotenuse}\\\\\\\tan \theta=\dfrac{opposite}{adjacent}\\\\\\\csc \theta=\dfrac{Hypotenuse}{opposite}\\\\\\\sec \theta=\dfrac{hypotenuse}{adjacent}\\\\\\\cot \theta=\dfrac{adjacent}{opposite}$

Now, we know that the side which is opposite to angle θ is of length: 9

The side which is adjacent to angle θ is of length: 12

and the hypotenuse of the triangle is: 15

Hence, we have:

$\sin \theta=\dfrac{9}{15}\\\\\\\cos \theta=\dfrac{12}{15}\\\\\\\tan \theta=\dfrac{9}{12}\\\\\\\csc \theta=\dfrac{15}{9}\\\\\\\sec \theta=\dfrac{15}{12}\\\\\\\cot \theta=\dfrac{12}{9}$