Intro to Trig

Intro to Trigonometry

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!

Identifying Sides!

You can't do trig if you can't define these terms:

Hypotenuse: Doesn't touch (across from) the right angle

Opposite: Doesn't touch (across from) the reference angle

Adjacent: Touches both the right angle and the reference angle

Multiple Choice

Which is the opposite to the angle A?

• a

• b

• c

Multiple Choice

Which is the opposite to the angle B?

• a

• b

• c

Multiple Choice

Which is the adjacent to the angle B?

• a

• b

• c

Multiple Choice

Which is the hypotenuse?

• a

• b

• c

Multiple Choice

Which is adjacent to angle A?

• a

• b

• c

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)

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

$$\sin\left(\angle S\right)$$  ?

• $$\frac{20}{29}$$  

• $$\frac{21}{20}$$  

• $$\frac{21}{29}$$  

Math Response

What is sin(B)?

Type answer here

Correct Answer: \frac{20}{29}

Deg^°

Rad

Math Response

What is cos(B)?

Type answer here

Correct Answer: \frac{21}{29}

Deg^°

Rad

Math Response

What is tan(B)?

Type answer here

Correct Answer: \frac{20}{21}

Deg^°

Rad

Cosecent, Secant, and Cotangent are Reciprocal Trig functions

Cosecent --> csc
Secent --> sec
Cotangent --> cot

Labelling

Find each trig ratio

Drag labels to their correct position on the image

20/21

29/21

29/20

21/29

21/20

20/29

Math Response

Find the cotangent of Angle A.

Type answer here

Correct Answer: \frac{8}{6}

Deg^°

Rad