Download 7.6 Apply the Sine and Cosine Ratios

7.6 Apply the Sine and Cosine Ratios Goal  Use the sine and cosine ratios.
SINE AND COSINE RATIOS
Let ΔABC be a right triangle with acute A.
The sine of A and cosine of A (written sin A and cos A) are
defined as follows:
sin A =
cos A =
length of leg opposite 
=
length of hypotenuse
length of leg adjacent to 
=
length of hypotenuse
Remember these
abbreviations:
sine → sin
cosine → cos
hypotenuse → hyp
Example: Find sin U and sin W. Write each answer as a fraction.
sin 𝑈 =
𝑜𝑝𝑝
ℎ𝑦𝑝
=
sin 𝑊 =
𝑜𝑝𝑝
ℎ𝑦𝑝
=
Example: Find cos S and cos R. Write each answer as a fraction
𝑐𝑜𝑠 𝑆 =
𝑐𝑜𝑠 𝑅 =
Example: Basketball You walk from one corner of a basketball court to the opposite
corner. Write and solve a proportion using a trigonometric ratio to approximate the
distance of the walk.
Step1: Determine which two sides are involved for the given ∠. (in this case opp and hyp)
Step2: Choose the appropriate trig function (in this case opp and hyp -> sin)
𝒔𝒊𝒏 𝟔𝟐°
Step3: Set up and solve a proportion.
𝟏
=
𝟗𝟒
𝒙
Angle of depression - When looking down at an object, the angle your line of sight makes with a horizontal line
is called the angle of depression.
Example: Roller Coaster You are at the top of a roller coaster 100 feet above the
ground. The angle of depression is 44°. About how far do you ride down the hill?
Step1:
Step2:
Step3:
Angle of elevation - When looking up at an object, the angle your line of sight makes with a horizontal line is
called the angle of elevation.
Example: Railroad A railroad crossing arm that is 20 feet long is stuck with
an angle of elevation of 35° Find the lengths x and y
Examples: Find the value of each variable. Round decimals to the nearest tenth.
What if you have the sides and want to find the angle? (AKA what undoes sine and cosine?)
(AKA What the heck is that 𝐬𝐢𝐧−𝟏 𝒂𝒏𝒅 𝐜𝐨𝐬 −𝟏 thing on my calculator?)
Step1: Identify sides for ∡𝑨
Step2: Set up appropriate ratio
Step3: “Undo” sin or cos with
𝐬𝐢𝐧−𝟏 𝒐𝒓 𝐜𝐨𝐬 −𝟏 on calculator
You Try (Find 𝒎∡𝑨):