Question

How do you calculate sin 67 degrees 40'?

Answer 1

Hint: In this question we have to find the value of the given trigonometric angle and we will do by using a calculator. First convert the minutes to degrees by using the formula ${1^o} = 60$ minutes. Then the calculation is done by pressing the SIN key in the calculator and the angle value here is 67 degrees 40’ , then we will get the required answer by pressing “ENTER”.

Complete step by step solution:
Given trigonometric angle is sin 67 degrees 40 minutes,
Now converting minutes to degrees by using the fact ${1^o} = 60$minutes,
So, here $ \Rightarrow 40' = {\left( {\dfrac{{40}}{{60}}} \right)^o}$,
Now simplifying we get,
$ \Rightarrow 40' = {\left( {\dfrac{2}{3}} \right)^o}$,
So, the given value becomes,
$ \Rightarrow \sin {\left( {67 + \dfrac{2}{3}} \right)^o}$,
Now simplifying we get,
$ \Rightarrow \sin 67.67$
Now to find the value we will use graphing calculator like T1-84,
To evaluate the trigonometric functions in the calculator we first press “SIN” key to enter, now we enter parenthesis and enter the given angle i.e., 67.67,
So, having entered all the values , we now press the “ENTER” key, after pressing the “ENTER” key the calculator immediately shows the answer as “ 0.92498” which is in degrees as the default mode of the calculator for angle measurements in degrees. We can also change the degrees to radians just by pressing the “MODE” key.
So, the value of sin 67 degrees and 40 minutes is 0.92498.

Final Answer:
$\therefore $The value of given trigonometric angles sin 67 degrees and 40 minutes will be equal to 0.92498.

Note:
The inverse trig functions are generally the second [2nd] functions of the trigonometry buttons in the calculator. We should also get in the habit of using the $\pi $ button instead of typing in 3.14159 ... for $\pi $. Most calculators don't have [sec], [csc] and [cot] functions because it's easy enough to type in$\dfrac{1}{{\sin x}}$, $\dfrac{1}{{\cos x}}$, or $\dfrac{1}{{\tan x}}$ . Make sure you always know which angle units your calculator is set to use: radians or degrees. Know how to switch between them.