Find the remaining trigonometric functions of θ if where m and n are both positive. Assume that θ is between 0° and 180°.

Question

Find the remaining trigonometric functions of θ  if   where m and n are both positive. Assume that θ  is between 0° and 180°.

Quizplus · Accepted Answer

From the given value of tangent, we can use the Pythagorean identity to find the value of the adjacent side:

$$	an(	heta) = \frac{m}{n} = \frac{4}{3} \Rightarrow 	ext{opposite} = 4, 	ext{adjacent} = 3$$

Using these values, we can now find the remaining trigonometric functions:

$$\sin(	heta) = \frac{	ext{opposite}}{	ext{hypotenuse}} = \frac{4}{5}$$
$$\cos(	heta) = \frac{	ext{adjacent}}{	ext{hypotenuse}} = \frac{3}{5}$$
$$\csc(	heta) = \frac{	ext{hypotenuse}}{	ext{opposite}} = \frac{5}{4}$$
$$\sec(	heta) = \frac{	ext{hypotenuse}}{	ext{adjacent}} = \frac{5}{3}$$
$$\cot(	heta) = \frac{1}{	an(	heta)} = \frac{n}{m} = \frac{3}{4}$$

Therefore, choice C is the correct answer.

Find the Remaining Trigonometric Functions of θ If Where