Question

(1) Write the maximum and minimum values of $\sin \theta$ .
(2) Write the maximum and minimum values of $\cos \theta$ .
(3) Write the maximum value of ${\displaystyle \frac{1}{\sec \theta }}$ ?
(4) Write the maximum value of ${\displaystyle \frac{1}{\cos ec\theta }}$ ?

Answer 1

Hint: Use the trigonometric value table and find the necessary values.
When we are going to find the maximum and minimum value, we will look at the trigonometric value table and then we can find them or else we can also find them by looking at the graph formed by the function given in the question (alternate method) for that we need to be familiar with graphs of all trigonometric functions.

Complete step by step solution:
(1)Write the maximum and minimum values of $\sin \theta$ .
The maximum value of $\sin \theta$ is 1, we get this value when $\theta ={90}^o$ and the minimum value of $\sin \theta$ is -1 which is formed when $$\theta ={270}^o$$. Which means that we have the interval of $$-1⩽sin\theta ⩽1$$.

(2) Write the maximum and minimum values of $\cos \theta$ .
The maximum value of $\cos \theta$ is 1, this is formed when $\theta =0^o,{360}^o$ and the minimum value of $\cos \theta$ is -1, this is formed when $\theta ={180}^o$ , which gives us the interval of $$-1⩽cos\theta ⩽1$$.

(3) Write the maximum value of ${\displaystyle \frac{1}{\sec \theta }}$ ?
We can write ${\displaystyle \frac{1}{\sec \theta }}$ as $\cos \theta$ , which means the both have the same maximum value which is the maximum value of $\cos \theta$ is 1, this is formed when $\theta =0^o,{360}^o$ .

(4) Write the maximum value of ${\displaystyle \frac{1}{\cos ec\theta }}$ ?
We can write ${\displaystyle \frac{1}{\cos ec\theta }}$ as $\sin \theta$ , which means they both have the same maximum value. Therefore, the maximum value of $\sin \theta$ is 1, we get this value when $\theta ={90}^o$ .

Note: To solve these problems, we need to be familiar and good with the table of trigonometric values. As these problems completely depend on them or else we need to remember the graphs of the given functions in the question.