Download 4.3 Right Triangle Trigonometry

4.3 Right Triangle Trigonometry
Objective: In this lesson you will learn how
to evaluate trigonometric functions of acute
angles and how to use the fundamental
trigonometric identities.
Ex 1) In the right triangle below, find the values of
the 6 trig functions.
8
θ
15
sin θ =
csc θ =
cos θ =
sec θ =
tan θ =
cot θ =
Ex 2) Find the values of the 6 trig functions if
tan θ = 3.
sin θ =
csc θ =
cos θ =
sec θ =
tan θ =
cot θ =
θ
Ex 3) Complete the missing information
function
csc
θ (deg)
θ (rad)
value
√2
Ex 4) Use the given information to find the
indicated trig functions.
csc θ = 3
a) sin θ =
b) cos θ =
c) tan θ =
d) sec (90º - θ) =
3 2
sec θ =
4
Ex 5) Use the trig identities to transform one side
of the equation into the other.
tan θ cos θ = sin θ
Ex 6) Use the trig identities to transform one side
of the equation into the other.
sin  cos

 csc sec
cos sin 
Ex 7) Use a calculator to evaluate each function.
Round your answer to 4 decimal places.
a) sec 1.54 =
b) cos 1.25 =
Ex 8) Find each value of θ (0 <θ ≤ 90º) in degrees
and radians (0 <θ ≤ /2) without using a
calculator.
a) csc θ=
2 3
3
b) sin θ =
2
2
Ex 8) Solve for x, y, or r as indicated.
38
60º
x