1. Table of Contents 5. Right Triangle Trigonometry

2. Right Triangle Trigonometry
Essential Question – How can right triangles help solve real world applications?

3. The Pythagorean theorem
In a rt Δ the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
c2 = a2+b2 c a __ b __

4. Example
x2=72+242
x2=49+576
x2=625 x
x=25 7 __ __ 24

5. Example __ __ x 12

6. 3 basic trig ratios Sine (sin) Cosine (cos) Tangent (tan) Sin  Cos 

7. SOH CAH TOA
Sin = opp/hyp
Cos = adj/hyp
Tan = opp/adj

8. Ex: Find sin, cos, & tan of A & B.
sin A= 12/13
cos A= 5/13
tan A= 12/5 12 C B B
sin B= 5/13
cos B= 12/13
tan B= 5/12 5 13 A

9. Inverse Trig Functions
Cosecant is the inverse of sin
Secant is the inverse of cos
Cotangent is the inverse of tan

10. Example: Six Trig Ratios
Given that , calculate the other trigonometric functions for  . 4 3 5 
Step 1: Draw a right
triangle and find
third side using
Pythagorean theorem.
Step 2: Find the other ratios using formulas.
sin  =
csc  =
cos  =
sec  =
tan  =
cot  =
Example: Six Trig Ratios

11. More examples Given that sin = 7/25, sketch the triangle
and find the third side. Then find cos
Given that tan = ¾, sketch the triangle
and find the third side. Then find sin
Given that tan = 4/5, what is cot ?

12. Given a point, find all trig functions
1. Draw right triangle
2. Label theta
3. Label sides
4. Use Pythagorean theorem to find missing side
5. Find all 6 functions

13. Example
Given the point (-4,10) find the values of the six trig function of the angle.
1. Plot point
(-4,10)
2. Draw rt triangle
3. Label angle
and sides
10.8 10
4. Use Pyt. Th.
to find 3rd side. -4
5. Find trig
functions

14. Example
Given the point (-5,-2) find the values of the six trig function of the angle.
1. Plot point
2. Draw rt triangle
3. Label angle
and sides -5
4. Use Pyt. Th.
to find 3rd side. -2
(-5,-2)
5. Find trig
functions

15. Last type of problem You are given a trig ratio
It can be in one of two quadrants
Therefore you have to be given another piece
of information to determine which quadrant it
is in

16. Always Study Trig Carefully
Sin y values
Cos x values
Tan sin/cos
Sin +
Cos -
Tan -
Sin +
Cos +
Tan +
Where are these positive?
Always
Sin
All
Study
Sin -
Cos -
Tan +
Sin -
Cos +
Tan -
Trig
Carefully
Tan
Cos

17. Steps 1. Find what quadrant the triangle is in
2. Draw right triangle, only sides will be negative,
hypotenuse will never be negative
3. Use Pythagorean theorem to find 3rd side
4. Find other trig functions

18. Example
Given that cos θ = 8/17 and tan θ < 0, find all six trig functions. 8 θ
-15 17
Triangle is in 4th quadrant because that is
where cos is positive and tan is negative