Download 4.2 notes trigonometric functions 6 trig functions sine θ = sin θ

4.2 notes trigonometric functions
6 trig functions
sine θ = sin θ =
cosecant θ = csc θ =
cosine θ = cos θ =
secant θ = sec θ =
tangent θ = tanθ =
cotangent θ = cot θ =
Don’t forget SOHCAHTOA
Using special right triangles to evaluate trig ratios (45-45-90 and 30-60-90)
sin 45 =
cos 45 =
tan 45 =
csc 45 =
sec 45 =
cot 45 =
sin 30 =
cos 30 =
tan 30 =
csc 30 =
sec 30 =
cot 30 =
sin 60 =
cos 60 =
tan 60 =
csc 60 =
sec 60 =
cot 60 =
Determining all 6 trig functions when you are only given 1
1)
2)
3)
4)
Draw a right triangle and label 1 of the non-right angles, θ
Label the given lengths appropriately
Use Pythagorean theorem to find the missing side
Find the remaining trig functions
Ex: 1) sin θ =
2) tan θ =
3) sec θ =
Evaluating on a calculator:
Need to make sure that you are in the correct mode. If the problem is given as sin 45˚, your calculator must in degree
mode (if you are in the wrong mode an answer will be given but it will be incorrect) . If the problem is given as sin , your
calculator must in radian mode (again if you are in the mode an answer will be given but it will be incorrect).
There are 4 common calculator errors on p. 332, make sure you read through them
Ex: 1. cos 8˚
2) tan 23˚ 42’
3) sin
4) csc 19˚
5) sec 1.24
6) cot
Find the acute angle θ that satisfies the given equation. Give θ in both degrees and radians. DO NOT use a calculator
(these will come from either one of the special right triangles)
Ex: 1. sin θ =
2. cos θ =
3. cot θ = 1
Solving a right triangle:
Use trig to solve right triangles. If the triangle isn’t drawn, draw
it
Ex:
1. solve the triangle for all of its unknowns.
a.
=
b. a = 5,
=
=
2. Kristen places her telescope on the top of a tripod 5 feet above the ground. She measures an 8˚ angle of elevation
above the horizontal to the top of a tree that is 120 feet away. How tall is the tree?
3. The Chrysler Building in New York City was the tallest building in the world at the time it was built. It casts a shadow
approximately 130 feet long on the street when the sun’s rays form an 82.9˚ angle with the earth. How tall is the building?