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

The first expression is given below as

Hence,

The answr for tan theta is

`tan\theta=(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=(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=(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=(1)/(tan\theta) \\ cot\theta=(cos\theta)/(sin\theta) \end{gathered}`
`cot\theta=(cos\theta)/(sin\theta)`