Inverse Trig

Finding the Angle in a Right Triangle

Using inverse trigonometry functions to solve for missing angles in a right triangle

The Process is EXACTLY the same

• Highlight the angle

• Based on the angle, identify the given parts as opposite, adjacent and hypotenuse

• Using the parts you know, which trigonometry equation can you use SIne, Cosine, or Tangent

• Write the equation and solve

• Solving for the angle requires you to use the INVERSE Opperation

Multiple Choice

Which is the correct equation for the diagram?

• $$\sin\left(\theta\right)=\frac{20}{25}$$  

• $$\cos\left(\theta\right)=\frac{20}{25}$$  

• $$\tan\left(\theta\right)=\frac{20}{25}$$  

• $$\sin\left(\theta\right)=\frac{25}{20}$$  

Fill in the Blanks

What is the answer rounded to three decimal places for   $\sin^{-1}\left(\frac{20}{25}\right)=$  

  

Multiple Choice

What is the correct equation that can be used to solve for Angle A?

• $$\sin\left(A\right)=\frac{10}{14}$$

• $$\cos\left(A\right)=\frac{10}{14}$$

• $$\tan\left(A\right)=\frac{10}{14}$$

• $$\tan\left(A\right)=\frac{14}{10}$$

Multiple Choice

We now know  $$\cos\left(A\right)=\frac{10}{14}$$  

So we have to use inverse cosine to solve it.   Which one below is correct?

• $$A=\sin^{-1}\left(\frac{10}{14}\right)$$

• $$A=\cos^{-1}\left(\frac{10}{14}\right)$$

• $$A=\tan^{-1}\left(\frac{10}{14}\right)$$

• $$A=\tan^{-1}\left(\frac{14}{10}\right)$$

Fill in the Blanks

What is the value of $\cos^{-1}\left(\frac{10}{14}\right)$  rounded to three decimal places?

Multiple Choice

What would you use to solve for x?

• Inverse sine

• Inverse cosine

• Inverse tangent

• Pythagorean Theorem

Multiple Choice

Solve for x

• $$x=\tan\left(\frac{8}{15}\right)$$

• $$x=\tan\left(\frac{15}{8}\right)$$

• $$x=\tan^{-1}\left(\frac{8}{15}\right)$$

• $$x=\tan^{-1}\left(\frac{15}{8}\right)$$

Fill in the Blanks

What is the value of $\tan^{-1}\left(\frac{8}{15}\right)$  rounded to three decimal places?

Multiple Choice

Which inverse trig function would you use to find the measure of Angle A?

• inverse sine

• inverse cosine

• inverse tangent

• It is not possible to determine m<A

Multiple Choice

Which is the correct solution for angle A?

• $$A=\sin\left(\frac{2}{10}\right)$$

• $$A=\sin\left(\frac{10}{2}\right)$$

• $$A=\sin^{-1}\left(\frac{2}{10}\right)$$

• $$A=\sin^{-1}\left(\frac{10}{2}\right)$$

Fill in the Blanks

What is the value of  $\sin^{-1}\left(\frac{2}{10}\right)$ rounded to three decimal places? 

Multiple Choice

Find the measure of the indicated angle.  

• $$\sin^{-1}\left(\frac{15}{16}\right)$$

• $$\cos^{-1}\left(\frac{15}{16}\right)$$  

• $$\tan^{-1}\left(\frac{15}{16}\right)$$  

• Cannot be determined

Fill in the Blanks

What is the value of  $\cos^{-1}\left(\frac{15}{16}\right)$  rounded to three decimal places?

Poll

I know the difference between sine and inverse sine?

• Yes

• I think I kind of understand but I am still confused

• No

Poll

I can write an equation with inverse trigonometry to solve for an angle

• Yes

• I think I kind of understand but I am still confused

• No

Poll

If I were given a problem that involved trigonometry, I know if I am supposed to use regular trigonometry or inverse trigonometry to solve the problem.

• Yes, I got this!

• I would be able to if you gave me a hint

• If you talked me through every step I could do it

• Even if you showed my an example and asked me to explain what you did I still would have not clue