Download 12.1 Notes

12.1
TRIGONOMETRIC FUNCTIONS
IN RIGHT TRIANGLES
 Recall from Geometry:
 Pythagorean Theorem: a2+ b2= c2
 SOH CAH TOA
Cos =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Opposite
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
 Sin=
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Adjacent
Angle
tan=
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
There are 3 more trig functions to know
Example 1
 Find the values of the six trigonometric
functions for angle G.
Example 2
 In a right triangle, A is acute and 𝐭𝐚𝐧 𝑨 =
Find the value of csc A.
𝟓
.
𝟑
Example 3
 In a right triangle, B is acute and 𝐬𝐢𝐧 𝑩 =
Find the value of cot B.
𝟐
.
𝟑
Find a missing side
 Example 4: Find the length of y.
Example 5
 Find the length of x.
Special Right Triangles
Example 6
 Find the exact value of x.
Example 7
 Find the exact value of x.
45 ͦ
x
5 3
Example 8
 A) Find the measure of A.
Round to the nearest tenth if
necessary.
 B. Find the measure of B.
Round to the nearest tenth if
necessary.
Example 9
 Find the measure of
A.
27
Example 10
A golfer is standing at the tee,
looking up to the green on a hill.
The tee is 36 yards lower than the
green and the angle of elevation
from the tee to the hole is 12°.
From a camera in a blimp, the
apparent distance between the
golfer and the hole is the
horizontal distance. Find the
horizontal distance.
Example 11
The hill of the roller coaster has an angle of descent, or
an angle of depression, of 60°. Its vertical drop is 195 feet.
From a blimp, the apparent distance traveled by the
roller coaster is the horizontal distance from the top of
the hill to the bottom. Find the horizontal distance.
Example 12
Mario hits a line drive home run from 3 feet in the air to a
height of 125 feet, where it strikes a billboard in the
outfield. If the angle of elevation of the hit was 22°, what
is the horizontal distance from home plate to the
billboard?
Example 6
 To calculate the height of a tree in his front yard,
Anand walked 50 feet from the base of the tree and
used an inclinometer to measure the angle from
his eye to the top of the tree, which was 62°.
If Anand’s eye level is at 6 feet, about how tall is the
tree?