Download Sine, Cosine and Tangent Introduction

Sine, Cosine and Tangent Introduction
We will now be studying trigonometry, or __________, for short. Trigonometry is the study of
triangles—how to find missing sides and angles. The three most common ratios in trigonometry
are_____________________________________________. You will use them a lot! We use the
phrase _______________________ to remind us which sides correspond to which trigonometric
ratio. These ratios are simply one side of a triangle divided by another. We use these ratios to
find missing sides and angles in right triangles.
For any angle "θ": (prounounced __________), the sine, cosine, and tangent ratios are:
Sine Function: sin(θ) =
Cosine Function:
Tangent Function:
cos(θ) =
tan(θ) =
Sine, Cosine and Tangent are often abbreviated to ______, ______, and ______.
Let’s find the sine, cosine, and tangent of the angles of 2 special right triangles. You will see
these 2 triangles quite a bit in Algebra 2.
*Regardless of the size of the triangle, the sine, cosine, and tangent ratios for an angle will
always be the same. So sin 30  0.5 will be the same no matter how big the triangle is.
Example: What is the sine, cosine, and tangent of 35°? Round your answers to 2 decimal places.
Using this triangle (lengths are only to one decimal place):
sin(35°) =
cos (35) =
tan (35) =
You can also use a calculator or trig table to find the sine, cosine, or tangent of any angle. We
usually use angles less than 180 because we do trigonometry mainly with triangles. Let’s see
how to find these ratios on our calculators.
Where are the sine, cosine, and tangent keys located on a calculator?
Use the trig table or calculator to find the sine, cosine, and tangent of the following angles.
*Be sure the “mode” is in degrees on the calculator…not radians!
For #1-3, compare your decimals to the fractions we found using the special right triangle
lengths.
1) 30
2) 45
3) 60
4) 35
5) 48
5) 90