Complementary Functions

Complementary Functions

Friday Feb. 19, 2021

Materials

You will 100% need your calculator today

and maybe some scratch paper if you like to track your thinking / work

Warm - up

Which one doesn't belong?

You will be given 1 minute to examine an image and decide which image doesn't belong. Then, on the following slide, you will state a reason why

Open Ended

Which image did you choose, and why?

More Practice

I know, this unit is crazy repetitive but we're only going to get better with more practice.

Multiple Choice

Solve for x:

• x = 9.3 units

• x = 5.4 units

• x = 10.4 units

• Not enough information

x = 9.3 units

• adjacent = 7, hypotenuse = x

•  $\cos\ =\ \frac{a}{h}$  

•  $\cos\left(41\right)=\frac{7}{x}$  

•  $x\cdot\cos\left(41\right)=7$  

•  $x=\frac{7}{\cos\left(41\right)}$  

•  $x=9.3$  

Multiple Choice

Solve for y:

• x = 9.3 units

• x = 5.4 units

• x = 10.4 units

• Not enough information

y = 5.4 units

• opposite = y, hypotenuse = 6

•  $\sin=\frac{o}{h}$  

•  $\sin\left(65\right)=\frac{y}{6}$  

•  $6\cdot\sin\left(65\right)=y$  

•  $5.4\ =\ y$  

• which means  $y=5.4$ 

Multiple Choice

Solve for z:

• x = 9.3 units

• x = 5.4 units

• x = 10.4 units

• Not enough information

z = 10.4 units

• opposite = 8, hypotenuse = z

•  $\sin=\frac{o}{h}$  

•  $\sin\left(50\right)=\frac{8}{z}$  

•  $z\cdot\sin\left(50\right)=8$  

•  $z=\frac{8}{\sin\left(50\right)}$  

•  $z=10.4$  

Some new notation

• to represent an acute angle, we will use the Greek letter theta

• Theta looks like this $\theta$ 

• We will also often use the Greek letter alpha

• Alpha looks like this  $\alpha$  

Multiple Choice

Alpha or theta?

 $\theta$  

• Alpha

• Theta

Multiple Choice

Alpha or theta?

 $\alpha$  

• Alpha

• Theta

Remember complementary angles?

• You know, the ones that add up to
  

   $90\degree$  ?

•  $10\degree\ and\ 80\degree$  

•  $77\degree\ and\ 13\degree$  

•  $\theta\ and\ 90-\theta$  ...?

Look at this image...

• Using this image decide if you agree, or disagree with the following statement (keep your answers to yourself for right now)

•  $\sin\left(\theta\right)=\cos\left(90-\theta\right)$  

• you will submit your answer on the next slide in just a moment

Fill in the Blanks

Agree or disagree?

 $\sin\left(\theta\right)=\cos\left(90-\theta\right)$  

It is actually true:

 $\sin\left(\theta\right)=\cos\left(90-\theta\right)$  

Remember when we used our tables and just switched the information in the columns (back before we knew trig)?

This is why we could do that.

Remember: this ONLY works with complementary angles

Open Ended

Find the value or expression for

 $\theta$  :

 $\sin\left(55\right)=\cos\left(\theta\right)$  

Open Ended

Find the value or expression for

 $\theta$  :

 $\sin\left(\theta\right)=\cos\left(28\right)$  

Open Ended

Find the value or expression for

 $\theta$  :

 $\cos\left(y\right)=\sin\left(\theta\right)$  

Complements

•  $35\degree$  

•  $62\degree$  

•  $\left(90-y\right)\degree$