Question

To further justify the Cofunction Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigon

Trigonometric Functions
ANSWERED
asked 2021-02-25
To further justify the Cofunction Theorem, use your calculator to find a value for the given pair of trigonometric functions. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point.
\(\displaystyle{{\sec{{6.7}}}^{\circ},}{\cos{{e}}}{c}{83.3}^{\circ}\)

Expert Answers (1)

2021-02-26
Use cofunction of the given trigonometric function,
\(\displaystyle{\sec{{x}}}={\cos{{e}}}{c}{\left({90}^{\circ}−{x}\right)}\)
Given,
\(\displaystyle{{\sec{{6.7}}}^{\circ}}\)
Here \(\displaystyle{x}={6.7}^{\circ}\)
\(\displaystyle{{\sec{{6.7}}}^{\circ}=}{\cos{{e}}}{c}{\left({90}^{\circ}−{6.7}^{\circ}\right)}\)
\(\displaystyle={\cos{{e}}}{c}{\left({83.3}^{\circ}\right)}\)
\(\displaystyle={1.006876}\)
\(\displaystyle\approx{1.0069}\)
Therefore \(\displaystyle{{\sec{{6.7}}}^{\circ}=}{1.0069}\)
Now use cofunction of the given trigonometric function,
\(\displaystyle{\cos{{e}}}{c}{x}={\sec{{\left({90}^{\circ}−{x}\right)}}}\)
Given,
\(\displaystyle{\cos{{e}}}{c}{\left({83.3}^{\circ}\right)}\)
Here \(\displaystyle{x}={83.3}^{\circ}\)
\(\displaystyle{\cos{{e}}}{c}{83.3}^{\circ}={\sec{{\left({90}^{\circ}−{83.3}^{\circ}\right)}}}\)
\(\displaystyle={{\sec{{6.7}}}^{\circ}}\)
\(\displaystyle={1.006876}\)
\(\displaystyle\approx{1.0069}\)
Therefore, \(\displaystyle{\cos{{e}}}{c}{83.3}^{\circ}={1.0069}\)
We clearly see that trigonometric functions are cofunction of one another.
Sum of the angles of two cofunctions is \(\displaystyle{90}^{\circ}\) that is the angles are complementary angles.
Therefore the pair of a trigonometric function is,
\(\displaystyle{\left({{\sec{{6.7}}}^{\circ},}{\cos{{e}}}{c}{83.3}^{\circ}\right)}={\left({1.0069},{1.0069}\right)}\)
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