Download Honors Trig Review

Honors Physics
Chapter 1
Trigonometry Review
We will be working with the sine, cosine, and tangent functions in this course. These
functions are defined for right triangles as follows:
sin  
Opposite
Hypotenuse
hypotenuse
cos 
adjacent
hypotenuse
opposite
θ
opposite
tan  
adjacent
adjacent
These relationships can be remembered with the pneumonic device, soh cah toa.
Examples
Use the trigonometric functions to find the missing lengths for the following triangle.
1.
x
5
30°
Look at the triangle and identify which sides you have. The side with a value of 5 is
opposite of the 30 degree angle. The side with the value of x is the hypotenuse. Now
select the trigonometric function that relates the opposite side and the hypotenuse.
sin  
Opposite
Hypotenuse
sin 30 
5
Solve this equation for x.
x
x  sin 30  5
5
x
sin 30
x  10
1
Honors Physics
Chapter 1
2.
For this triangle the sides are the adjacent side and the
hypotenuse. Therefore, we use the cosine function.
40°
x
12
x
12
x  12  cos 40
x  9.19
cos 40 
x
12
12×tan25°=x
x=5.6
tan25°=
3.
x
25°
12
This is how we use the trigonometric functions to find the length of the sides of a right
triangle. We can also use it to find the angles in a triangle.
Examples – Find the value for the angle, θ, in each of the following problems.
1.
θ
12
Identify the sides that are known. In this problem
we know the side that is opposite of θ and the
hypotenuse. This means that we choose the sine
function.
8
8
12
In order to solve this equation, we must use the inverse trigonometric functions. We take
the inverse sine (sin-1) of both sides of the equation.
sinθ=
sin -1 (sinθ) =sin -1 (
8
)
12
θ = 42°
2
Honors Physics
Chapter 1
3
θ
4
Find the value of θ and the length of the
missing side of the triangle.
2.
θ
8
2
Find the value of θ.
3.
More Trig Review Problems
θ
8.0
6.0
1.
Solve for θ and missing side of triangle.
3
Honors Physics
Chapter 1
y
12
20.0°
2.
Solve for y and
missing side of triangle.
50°
4.5
x
3.
Solve for x.
θ
3.1
4.
6.4
Solve for θ.
4
Honors Physics
Chapter 1
14
θ
10
Solve for θ.
5.
60
z
5.0
6.
Solve for z.
0.577
θ
1.0
Solve for θ.
7.
5