Download 5.2 Right Triangle Trigonometry Trigonometry is all about ratios and

5.2 Homework:
5.2a and 5.2b on Math XL
5.2 Right Triangle Trigonometry
Trigonometry is all about ratios and triangles. The inputs of
these functions are acute angles in right triangles and the
outputs are ratios of the lengths of other sides of the triangle.
There are six possible trigonometric functions:
We often abbreviate the sin, cos, and tan with:
SOH-CAH-TOA
Similarly we can abbreviate csc, sec, and cot with:
CHO-SHA-CAO
But sadly that one is much less popular. It’s like the Crocs of
the high-fashion world of trig.
1.
Find the value of all 6 trig functions of 𝜃 in the following
triangle:
2.
2
Given sin 𝜃 = , find the five remaining trig functions.
3
3.
Use your calculator to evaluate to the nearest thousandth.
Make sure you are in the correct mode!
a.
sin 38.3°
b.
tan
c.
sec 53.2°
d.
cot 12.3°
e.
csc
𝜋
3
𝜋
4
You probably remember doing problems like this in geometry:
4.
A plane ascends with an angle of elevation of 15°. What
will be the plane’s horizontal distance from the runway
when it reaches its target elevation of 30,000 feet?
5.
An isosceles triangle’s base angles measure 31° and its
base length is 10 cm. Find the length of the legs.
6.
A swimming pool is 30 meters long. The bottom of the
pool is slanted so that the water depth is 1.3 meters at the
shallow end and 4 meters at the deep end. Find the angle
of depression of the bottom of the pool.
Special Right Triangles
7.
Use special right triangles to determine the following
common trig ratios.
a. sin 60°=
b. cos 60°=
c. sin 30°=
d. cos 30°=
e. sin 45° =
f. cos 45° =
FUNdamental Identities in Trig:
WEIRD NOTATION ALERT:
8.
Use trig identities to find the value of each expression (no
calculator!).
a. csc 44° ∙ tan 44° ∙ cos 44°
b.
𝜋
𝜋
3
3
sin2 + 2 + cos2
Cofunctions
Observe the following:
𝑏
sin 𝐵 = = cos 𝐴
𝑐
𝑏
tan 𝐵 = = cot 𝐴
𝑎
csc 𝐵 =
𝑐
= sec 𝐴
𝑏
9.
Find a cofunction with the same value as the given
expression:
a. sin 64°
b.
csc
𝜋
c.
cot
𝜋
3
4
10.
Use trig identities and cofunctions to find the value of
each expression (no calculator!).
cos 70°
a. tan 20° −
cos 20°
b.
cos 35° sin 55° + cos 55° sin 35°
c.
d.
1 + tan2 5° − csc 2 85°
1
𝜋
cot
4
+
2
𝜋
6
csc