Question

Express each function as a ratio in terms of sin 0, cos 0 or bothA) tan 0=B) csc 0=C) sec 0=D) cot 0=

Answer 1

Solution:

The first expression is given below as

Hence,

The answr for tan theta is

$tan\theta=\frac{sin\theta}{cos\theta}$

Step 2:

Cosecant:

We know that the cosecant function is the reciprocal of the sine function. So, the cosecant formula in terms of sine is given by, cosec x = 1/sin x.

Hence,

The final answer is

$csc\theta=\frac{1}{sin\theta}$

Step 3:

Secant:

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

Hence,

The final answer is

$sec\theta=\frac{1}{\cos\theta}$

Step 4:

Cotangent:

The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x .It is the reciprocal of tan theta

Hence,

The final answer is

$\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ cot\theta=\frac{cos\theta}{sin\theta} \end{gathered}$$cot\theta=\frac{cos\theta}{sin\theta}$