Algebra 2/Trigonometry
Mrs. Kushnir
Unit 9: Intro to Trigonometry
Essential Questions for this Unit:
How do the angle measures in a right triangle affect various ratios of the sides of the triangle?
What are the different ways we can measure an angle?
As a point travels around a unit circle, what patterns come to light in terms of its' horizontal and
vertical position?
Day
Topic/Activity
1
Right Triangle Trig Ratios
Reciprocal Trig Functions
Converting decimals to degree, minutes
and seconds and vice versa.
2
Angles as Rotations;
Trig Functions as Coordinates; Evaluating
Trig Functions on Calculator
Trig on the Unit Circle;
Exact Trig Function Values for Special
Angles
3
4
Radian Measure
Trig Functions of Angles in Radians
5
Trig Functions on the
Non-Unit Circle
6
Co-functions
7
Review
8
Unit Test
Suggested Homework
pp.796-797 (1, 3, 4 - 8, 28 - 40even)
Also do the following:
1) Convert the following 4 decimal places
a. 37°42’16”
b. 48°33’12”
2) Convert to degrees/minutes
(round to the nearest minute)
a. 96.265
b. 43.375
3) In ABC , m C  90o , m A  40o13' ,
and AB = 10. Find AC to the nearest
10th.
pp. 722-723 (1-19 odd, 29-35 odd, 47-52)
AND Day 2 HW sheet
pp. 722-723 (22 – 28 even, 57, 58, 60)
pp. 766-767 (1- 19 odd, 42-45)
ALSO, find the EXACT value of…
1) sec 120
2) cos 210 3) tan 300
pp. 729-731 (2 - 22 even, 29, 37-41 odd)
pp. 766-767 (22-28 even)
ALSO, find the EXACT value of…
 3 
 2 
1) csc  
2) cot  


 4 
 3 
 11 
 5 
3) sec 
4) tan 


 6 
 4 
Day 5 HW sheet AND
pp. 729 – 731 (5 – 11 odd, 30, 36 – 42
even, 47 – 48)
Day 6 HW sheet AND
p. 731 (43)
p. 766 (12 – 18, 21, 25)
Study!!
Trig Function Values chart due on Day 1
of next unit.
Day 2 Homework
1. In the figure, OA = 1, and m COA = . Name the line segment whose length (or directed
distance) is equal to…
a) sin 
b) cos 
c) tan 
2. Name the quadrant in which
A terminates:
a) Sin A < 0, Cos A > 0
b) Sin A > 0, Tan A > 0
c) Cos A < 0, Sin A < 0
3. If (sin )(cos ) > 0, name all the quadrants in which angle  can terminate.
4. Points A(1, 0) and B(.6, -.8) lie on a unit circle O. If m
a) sin =
b) cos =
AOB = , find:
c) tan =
5. Points R (1, 0) and P (-4/5, -3/5) lie on a unit circle O. If m
a) sin =
b) cos =
ROP = , find:
c) tan =
6. If tan  < 0 and sin  = .7, then  terminates in which quadrant?
7. Evaluate the following to 4 decimal places using a calculator:
a) csc 50
b) cot 200
c) sec 68o15’
1
Day 5 Homework
1. If  is acute, find  to the nearest 10th of a degree AND to the nearest minute:
a) csc  = 2.45
b) cot  = .4499
2. Based on the diagram shown, find:
a) sin  =
b) cos =
c) tan =
d) csc =
e) sec =
f) cot =
3. If tan A = 
3
and cos A < 0, find each of the following:
4
a. sec A
4. If sin B = 
b. cos A
c. sin A
d. csc A
e. cot A
5
and tan B >0, find each of the following :
13
a. cos B
5. If csc A = 
a. cot A
6. If sin A =
7. If tan A = 
a.
 15
b. tan B
c. cot B
d. csc B
e. sec B
10
and cot A < 0, find each of the following:
3
b. sin A
c. tan A
d. sec A
e. cos A
24
and sec A > 0, find tan A.
7
1
and cos A < 0, then sin A equals:
3
10
10
b. 
3
10
c. 
2
10
10
d.
3 10
10
Day 6 Homework
1. Write the expression as a function of an acute angle measuring less than 45°.
a) cot 65°
b) csc 58°
c) cos 75°
d) sin 280°
e) tan 265°
f) cot 95°
g) cos 258°
2. Find a value of  ( 0    90 ) for which the statement is true.
a) sin  = cos 
b) tan  = cot 5
c) sin 2 = cos ( + 15°)
d) tan ( + 5°) = cot (2 - 20°)
3. If x and y are the measures of two acute angles and tan x = cot y, then:
a. x = y + 90°
b. x = y - 90°
c. x = 90° - y
d. y = x - 90°
5. If  is acute and cos  = sin 60°, then cos  equals:
a. 30°
6. If
c.
3
2
d.
1
2
x is acute and sin (x + 15°) = cos 45°, then sin x equals:
a.
7. If
b. 60°
1
2
r and
b.
2
2
c.
3
2
d. 30°
t acute angles such that m r + m t = 90°, then cos r equals:
a. sin (90° - t)
b. sin (t + 90°)
c. sin(t - 90°)
3
d. sin t
8. If
b is acute and cos b = .75, then:
a. sin(b - 90°) = .75
b. sin(90° - b) = .75
c. sin b = .75
d. sin b = .25
9. Given: k is acute and cos k = sin (2k + 30°).
Demonstrate that m k may be 20° or 60°.
10. Given:  terminates in quadrant 1. Find  to the nearest minute if…
a) sec  =3.52
b) cot  = 5
11. Find the exact value of…
a) cos 225o
7
b) cot  
 6 
c) sec   240o 
4
5
d) tan  
 2 