Trigonometry Concepts Test

Trigonometry Concepts Test

Let's treat this as another pre-test before the quiz on Friday and the subsequent test on Tuesday. This will focus more on the concepts than straight calculation.

Concept 1 -

Drawing Angles

1. The initial side points right on the x-axis

2. The terminal side is where the angle ends.

3. Positive angles rotate counter-clockwise

4. Coterminal means two angles start and end on the same lines.

Multiple Select

Which of the following angles are drawn correctly?

Multiple Choice

• This is a positive angle.

• This is a negative angle.

Multiple Choice

Which of the following is coterminal to the angle drawn to the left.

Concept 2 -

Radians

• Remember a radian is just another unit for angles. Just like how yards and feet are both units of length, radians and degrees are both units for angles.

• There are 2π radians in   $360^o$ , which means there are  $\pi$ radians in  $180^o$  
   

• To switch from degrees to radians, we multiply by  $\frac{\pi\ radians}{180^o}$  

Multiple Choice

Which of the following is correct?

Multiple Choice

If I want to convert $135^o$ into radians, I should multiple 135 by ... 

•  $\frac{\pi}{180}$  

•  $\frac{180}{\pi}$  

Multiple Choice

If I want to convert $\frac{\pi}{6}\ radians$ into degrees, I should multiple  $\frac{\pi}{6}$  by ... 

•  $\frac{\pi}{180}$  

•  $\frac{180}{\pi}$  

Concept 3 -

Special Right Triangles

• In geometry we learned about two special right triangles: 30-60-90's and 45-45-90's. The next two slides go over these special triangles and their side lengths when they're drawn in a unit circle.

• These should be memorized before the quiz. This is me telling you - you need to know this, there will be a question on it.

30-60-90

• Things to memeorize:

• The hypotenuse = 1

• Opposite of the 30 =  $\frac{1}{2}$  

• Opposite of the 60 =  $\frac{\sqrt{3}}{2}$  

45-45-90

• Things to memeorize:

• The hypotenuse = 1

• Opposite of both 45's =  $\frac{\sqrt{2}}{2}$ 

Multiple Choice

How long are the sides in red?

• 1

• $\frac{1}{2}$

• $\frac{\sqrt{3}}{2}$

• $\frac{\sqrt{2}}{2}$

Concept 4 - 

Signs for Soh-Cah-Toa

• The important thing to remember is that $\sin\left(\theta\right),\ \cos\left(\theta\right)\ \&\ \tan\left(\theta\right)$  are not always positive. 

• I'll go over the mnemonic tool I gave you all once more on the next page. 

All Students Take Classes

The important thing to remember is that if you're asked to find the sin of an angle, for example, it is ONLY positive if the angle is in quadrants 1 or 2 (aka, above the x-axis).

Multiple Select

For which of the following angles will the $\sin\left(\theta\right)$ be positive? 

Multiple Select

For which of the following angles will the $\cos\left(\theta\right)$ be positive? 

Multiple Select

For which of the following angles will the $\tan\left(\theta\right)$ be positive? 

Multiple Choice

Which of the following is the mnemonic tool Mr. Hale has given us?

• All Students Can't Text

• All Classes Tire Students

• All Tests Students Cry

• All Students Take Classes

Concept 5 - Pythagorean Identity

No matter what the angle  $\theta$  is, the following equation is always true. 

 $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$  

Aka, if I know the  $\sin\left(\theta\right)$ , I can figure out  $\cos\left(\theta\right)$ , using this equation, and vice versa. 

Example

One problem, start to finish trying to find the $\sin\left(\theta\right)$  

Fill in the Blanks

If $\cos\left(\theta\right)=0.243$ and we're in the 4th quadrant, what is  $\sin\left(\theta\right)$ ?