Question

TRIGONOMETRY Review!

nometric Ratios: Find each trig rolio, Gve your answer as a fraction in simplest form.

Answer 1

The each trigonometry ratio can be expressed as

1.
`sin R=(5)/(13)`

2.
`Cos R =(12)/(13)`

3.
`Tan R=(5)/(12)`

4.
`sin T=(36)/(39) =(12)/(13)`

5.
`Cos T = (5)/(13)`

6.
`Tan T=(12)/(5)`

What is the trigonometry ratio?

Using Pythagoras theorem,

`c^(2) =a^(2) +b^(2)`

`c^(2) =36^(2) +b^(15)`

`c= √(1521) \\\\c= 39`

c= H = 39

Then we can attend to the trig ratio as;

1. sin R =opposite/hypotenuse

`sin R=(15)/(39) =(5)/(13)`

2. Cos R = adjacent/hypotenuse

`Cos R =(B)/(H)=(36)/(39) =(12)/(13)`

3. Tan R =opposite / adjacent

`Tan R =(P)/(B) =(5)/(12)`

4. sin T =opposite/hypotenuse

`sin T=(36)/(39) =(12)/(13)`

5.
`Cos T = (5)/(13)`

6.
`Tan T=(12)/(5)`

Answer 2

Find H

`\\ \rm\rightarrowtail H^2=36^2+15^2`

`\\ \rm\rightarrowtail H^2=39^2`

`\\ \rm\rightarrowtail H=39`

Now

`\\ \rm\rightarrowtail sinR=(P)/(H)=(15)/(39)=(5)/(13)`

`\\ \rm\rightarrowtail cosR=(B)/(H)=(36)/(39)=(12)/(13)`

`\\ \rm\rightarrowtail tanR=(P)/(B)=(5)/(12)`

`\\ \rm\rightarrowtail sinT=(36)/(39)=(12)/(13)`

`\\ \rm\rightarrowtail cosT=(5)/(13)`

`\\ \rm\rightarrowtail tanT=(12)/(5)`