Pythagorean Theorem and Trig Functions

Pythagorean Theorem

Reviewing important information needed for Trigonometry

The Pythagorean Theorem

Hypotenuse

• The longest side of a right triangle

• The side that is opposite (across) from the 90^o angle.

• When using the Pythagorean Theorem, the Hypotenuse is represented by the variable, c.

Fill in the Blanks

How long is the hypotenuse of this triangle?

Leg (of a Triangle)

• The two shorter sides of a right triangle

• The sides that are adjacent to the 90^o angle.

• When using the Pythagorean Theorem, the Legs are represented by the variables, a & b.

Right Triangle

• A right triangle is a triangle with a right angle in it (an angle that is 90^o)

• A triangle can be shown to have a 90^o angle by using a box.

• A right triangle will ALWAYS satisfy the Pythagorean Theorem

•  $a^2+b^2=c^2$  

Is it a Right Triangle?

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is this a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 12, 9, and 15 a right triangle?

• Yes

• No

Multiple Choice

Is a triangle with side lengths of 7, 4, and 4 a right triangle?

• Yes

• No

Multiple Choice

Find the missing side.

• 18

• 16

• 17

• 19

Multiple Choice

Find the missing side.

• 11

• 12

• 13

• 14

Multiple Choice

A triangle has legs that are 7 inches and 24 inches long. How long is the hypotenuse?

• 23

• 26

• 28

• 25

Multiple Choice

Which one is one of the easy ways to learn trigonometric ratios?

• Sah Coh Toa

• Soh Cah Toa

• Soh Cah Tao

• Soh Ceh Toa

Multiple Choice

Choose the correct ratio.

• sinZ=5/13

• sinX=5/13

• cosX=13/12

• tanZ=12/5

Multiple Choice

If you are given the opposite side and hypotenuse, which trig function should you use?

• sine

• cosine

• tangent

• cotangent

How do we use trig functions to find missing side?

• Step 1: Identify the given angle

• Step 2: Label opp, adj, and hyp based on given angle

• Step 3: Identify the appropriate trig function to solve for the missing side

• Step 4: Plug in given values and solve

Multiple Choice

Which equation would you use to solve for x?

• sin 62 = 10/x

• tan 62 = 10/x

• tan 62 = x/10

• cos 10 = x/62

Multiple Choice

Which ratio would you use to solve for x?

• sine

• cosine

• hypotenuse

• tangent

Multiple Choice

Set up the problem to solve for x.

• sin(47) = x/28

• cos(47) = x/28

• tan(47) = x/28

• cos(47) = 28/x

The Reciprocal Functions

• The three main trigonometric function values are ratios and ratios have reciprocals.

• The reciprocal of sine is COSECANT (CSC).

• The reciprocal of cosine is SECANT (SEC)

• The reciprocal of tangent is COTANGENT (COT)

So if they are reciprocals of one another

• If sinA = 3/5 then cscA = 5/3

• If cosA = 4/5 then secA =5/4

• If tanA = 3/4 then cotA = 4/3

Summary

Multiple Choice

what is sec(θ)

• 12 / 13

• 5 / 15

• 15/ 5

• 13 / 12

Multiple Choice

The GEOMETRY use of TANGENT;

Find the trig value. Take note you are looking for the tangent of angle C.

• A

• B

• C

• D

Multiple Choice

Let's practice some reciprocals...

Given $$\frac{5}{9}$$ , the reciprocal would be ___.

• $$\frac{9}{5}$$

• $$\frac{5}{9}$$

• Neither of these

Multiple Choice

Let's practice some reciprocals...

Given $$\frac{15}{7}$$ , the reciprocal would be ___.

• $$\frac{7}{15}$$

• $$\frac{15}{7}$$

• Neither of these

Multiple Choice

What is the reciprocal of the sine (sin) function?

• cosecant (csc)

• cosine (cos)

• secant (sec)

• cotangent (cot)

Multiple Choice

Cotangent (cot) is the reciprocal of what function?

• Cosecant (csc)

• Sine (sin)

• Cosine (cos)

• Tangent (tan)

Multiple Choice

What is the reciprocal of the cosine (cos) function?

• cosecant (csc)

• cosine (cos)

• secant (sec)

• cotangent (cot)