Question

How do you use a calculator to evaluate \[\cot {15^ \circ }14'\]?

Answer 1

Hint: Here we have to calculate the given term by using some calculation. On doing some simplification, we divide the particular value to get the value of degree itself. Then putting the value and simplify, we get the required answer.

Complete step by step answer:
It is given that, \[\cot {15^ \circ }14'\].
We have to evaluate \[\cot {15^ \circ }14'\] using a calculator.
First, we have to take the calculator in degree mode.
The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends, one radian is \[\dfrac{{180}}{\pi }\] degrees, or just under \[{57.3^ \circ }.\]
Then, divide, \[14\] by \[60\]. It converts \[14\] minutes into degrees.
With the division, we will add \[{15^ \circ }\].
After the addition, we will get \[15.2333...\] as the value.
Next, we find the tangent function of the given number.
So, we have, \[\tan (15.233...) = 0.27231880\]
We know that, \[\cot \theta = \dfrac{1}{{\tan \theta }}\]
For the calculator, we use \[\dfrac{1}{x}\] key.
So, we have the value as \[3.672166\].

Hence, \[\cot {15^ \circ }14' = 3.672166\].

Note: A calculator is a machine which allows people to do math operations more easily. For example, most calculators will add, subtract, multiply and divide. Some also do square root, and more complex calculators can help with calculus and draw function graphs.
Radian describes the plane angle subtended by a circular arc, as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius of the circle.
More generally, the magnitude in radians of such a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \[\theta = \dfrac{s}{r}\], where \[\theta \] is the subtended angle in radians, s is arc length, and r is radius. Conversely, the length of the enclosed arc is equal to the radius multiplied by the magnitude of the angle in radians; that is, \[s = r\theta \]