Introduction to Trig Ratios

Introduction to Trig Ratios

What To Do When the Pythagorean Theorem Just Won't Cut It!

Why Do We Need Trigonometry?

• Sometimes, we aren't given enough information to use the Pythagorean Theorem.

• Sometimes, we need to find angle measures with only the right angle given!

Where is trigonometry used in the real world?

* Video Game Design

* Speaker Placement in Concert Venues

* Architecture/Construction

* Criminology

* Military

The Basics

* Trigonometry only works with RIGHT triangles in Geometry.

* Given a specific angle (reference angle), you need to label the sides of the triangle as being opposite of, adjacent to (which means next to), or the hypotenuse, which is ALWAYS across from the right angle!

Notice This!

* The hypotenuse will ALWAYS be labelled as the hypotenuse-no matter where it is in relation to the reference angle.

* Which sides are opposite and adjacent depends on which angle is the reference angle.

*HELPFUL HINT! If you highlight the entire reference angle, those sides will ALWAYS be the hypotenuse and the adjacent sides!

Multiple Choice

What is the side ADJACENT to the reference angle?

• RT

• TK

• RK

Multiple Choice

Which is the side OPPOSITE of the reference angle?

• GN

• GW

• WN

Multiple Choice

Which side is the HYPOTENUSE of the triangle?

• KT

• KR

• TR

Trigonometric Ratios

The ratios formed by the side lengths of a right triangle.

*We use these to solve for missing sides and/or missing angles of right triangles.

sine (sin)

 $\frac{opposite}{hypotenuse}$  
The sin function is the ratio of the 
length of the side opposite the reference angle over the length of the hypotenuse.

cosine (cos)

The cosine of an angle is the ratio of the length of the side ADJACENT to the reference angle to the length of the HYPOTENUSE.

tangent (tan)

The tangent is the ratio of the side OPPOSITE the reference angle over the length of the side ADJACENT to the reference angle.

How Will I Remember All of Those Ratios?????

Here's How!

Multiple Choice

Which ratio represents

 $\cos\left(\angle W\right)$  ?

•  $\frac{8}{15}$  

•  $\frac{15}{17}$  

•  $\frac{8}{17}$  

Multiple Choice

Which ratio represents

 $\tan\left(\angle W\right)$  ?

•  $\frac{8}{17}$  

•  $\frac{15}{17}$  

•  $\frac{8}{15}$  

Multiple Choice

Which ratio represents

 $\sin\left(\angle S\right)$  ?

•  $\frac{20}{29}$  

•  $\frac{21}{20}$  

•  $\frac{21}{29}$  

Multiple Choice

Which ratio represents

 $\cos\left(\angle S\right)$  ?

•  $\frac{21}{20}$  

•  $\frac{21}{29}$  

•  $\frac{20}{29}$  

Multiple Choice

Which ratio represents


 $\tan\left(\angle S\right)$  ?

•  $\frac{20}{21}$  

•  $\frac{21}{29}$  

•  $\frac{21}{20}$