 # 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 iohanetc 2021-02-25 Answered
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.
${\mathrm{sec}6.7}^{\circ },\mathrm{cos}ec{83.3}^{\circ }$
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it grbavit
Use cofunction of the given trigonometric function,
$\mathrm{sec}x=\mathrm{cos}ec\left({90}^{\circ }-x\right)$
Given,
${\mathrm{sec}6.7}^{\circ }$
Here $x={6.7}^{\circ }$
${\mathrm{sec}6.7}^{\circ }=\mathrm{cos}ec\left({90}^{\circ }-{6.7}^{\circ }\right)$
$=\mathrm{cos}ec\left({83.3}^{\circ }\right)$
$=1.006876$
$\approx 1.0069$
Therefore ${\mathrm{sec}6.7}^{\circ }=1.0069$
Now use cofunction of the given trigonometric function,
$\mathrm{cos}ecx=\mathrm{sec}\left({90}^{\circ }-x\right)$
Given,
$\mathrm{cos}ec\left({83.3}^{\circ }\right)$
Here $x={83.3}^{\circ }$
$\mathrm{cos}ec{83.3}^{\circ }=\mathrm{sec}\left({90}^{\circ }-{83.3}^{\circ }\right)$
$={\mathrm{sec}6.7}^{\circ }$
$=1.006876$
$\approx 1.0069$
Therefore, $\mathrm{cos}ec{83.3}^{\circ }=1.0069$
We clearly see that trigonometric functions are cofunction of one another.
Sum of the angles of two cofunctions is ${90}^{\circ }$ that is the angles are complementary angles.
Therefore the pair of a trigonometric function is,
$\left({\mathrm{sec}6.7}^{\circ },\mathrm{cos}ec{83.3}^{\circ }\right)=\left(1.0069,1.0069\right)$

We have step-by-step solutions for your answer! Jeffrey Jordon

Answer is given below (on video)

We have step-by-step solutions for your answer!