Question

How do you use a calculator to approximate \[\arccos ( - 0.7)\] ?

Answer 1

Hint: “Arccos” stands for arccosine function. The arccosine function is the inverse function of \[\cos (x).\] It can be calculated using formulas and graphs or even with a calculator. To solve it with the help of a calculator, we require scientific calculators as basic calculators cannot handle trigonometric calculations.

Complete step by step solution:
The arccosine of \[x\] is defined as the inverse cosine function of \[x\] when \[ - 1 \leqslant x \leqslant 1\] .
When the cosine of \[y\] is equal to \[x\] :
 \[\cos y = x\]
Then the arccosine of \[x\] is equal to the inverse cosine function of \[x\] , which is equal to \[y\] :
 \[\arccos \,x = {\cos ^{ - 1}}x = y\]
For example, If the cosine of \[{60^ \circ }\] is \[0.5\] :
 \[\cos ({60^ \circ }) = 0.5\]
Then the arccos of \[0.5\] is \[{60^ \circ }\] :
 \[\arccos (0.5) = {\cos ^{ - 1}}0.5 = {60^ \circ }\]

We can proceed to calculate arccos in calculator as follows:
Step 1: Decide how you want your final answer to be displayed – whether in degrees or radiant and set the calculator mode accordingly.

Step 2: After deciding the mode, press \[\cos \] on a calculator such that it calculates \[{\cos ^{ - 1}}\] . We can generally access \[{\cos ^{ - 1}}\] easily on a calculator by pressing a button called \[2ND\] .

Step 3: Press the value for which you want to find the arccos. In the given case, press \[ - 0.7\] .

Step 4: Press Enter.
The calculator will display the final answer as per the pre-set format as follows:
In degrees the answer will be:
 \[\arccos ( - 0.7) = \pm {134^ \circ }42\]
In radians the answer will be:
 \[\arccos ( - 0.7) = \pm 2.3462\]

Note: Here \[{\cos ^{ - 1}}x\] means the inverse cosine and does not mean cosine to the power of \[ - 1\] .
The formula for arccos of negative argument is as follows:
 \[\arccos ( - x) = \pi - \arccos \,x = {180^ \circ } - \arccos \,x\]
Remember to set the mode on your calculator and only then proceed to solve the sum.