
How do you find the exact value of ?
Answer
461.4k+ views
Hint: We solve the given problem with the help of a graphing calculator. This is done by pressing the “ ” key followed by the “ ” key and then the value “ “. After pressing the “ ” key, we get the answer.
Complete step by step answer:
In the given problem, we have to find the value of at which is . We can do this on a graphical calculator like the calculator. The calculator provides a direct program to find the inverse trigonometric functions.
To evaluate the inverse trigonometric functions on , we at first press the “ “ key to activate the alternative function of a key. We now press the “ ” key to enter the function as the “ ” already activated the inverse operator before. Now, we can either enter a parenthesis or not enter it as both will yield the same answer is this case. We now press the “ ” key followed by pressing the “ “ key to enter .
Having entered all the values, we now press the “ ” key. After pressing the “ ” key, the calculator immediately presents the answer “ ” which is in degrees as the default mode of the calculator for angle measurements in degrees. We can change the settings to radian by pressing the “ ” key.
Now, the range of is and our answer is . Therefore, we can conclude that the exact value of is .
Note:
We should keep mind the range of various trigonometric functions like and should write the answers within that range only. The calculator always shows the answer which is closest to the and therefore, we should transform these values to the values within range. This problem can also be solved by plotting the graph of and drawing another line . The point of intersection within the region $\left( -{{90}^{\circ }}
Complete step by step answer:
In the given problem, we have to find the value of
To evaluate the inverse trigonometric functions on
Having entered all the values, we now press the “
Now, the range of
Note:
We should keep mind the range of various trigonometric functions like
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