Download MTH 114 Review Topics

MTH 114 Review Topics for Exam 1
Given an angle, be able to
- draw the angle in standard position. Know what quadrant the terminal side is in.
- convert to degrees, DMS or radians given another angle form both by hand and on
calculator
- find angles complementary or supplementary to the given angle
- Find several angles coterminal to the given angle
- Find the reference angle
- Find the EXACT value of all trig functions of an angle that is coterminal to angles on the
unit circle
- Find the coordinates of the point on the unit circle if the angle is coterminal to an angle
on the unit circle.
- Determine the quadrant and sign of trig functions
- Approximate the value of any trig function of the angle on a calculator
Given trig (angle) = #
- Find the exact value of angle in [0, π) or [0, 360° )
- Find the exact value of other trig functions at angle given information about the quadrant
using BOTH triangles and ID’s
- Find the value of other trig functions at other angles such as trig(-angle), trig(angle + π),
trig(π -angle), trig(π /2 – angle), trig(angle + 2k π) etc
Given a reference angle
- find an angle in any quadrant with that reference angle
Given a point on the terminal side of theta
- find the exact value of all 6 trig functions
Identities & Definitions:
- Know the basic Trig ID (reciprocal, Pythagorean, even/odd, cofunction etc) and how to
use.
- Know the definitions of basic terminology (angle, standard position , cofunction,
complementary, supplementary, coterminal angles, reference angle, unit circle,
hypotenuse, right angle, central angle etc.)
- Know the definitions of all trig functions (as ratios if sides of a right triangle)
UNIT CIRCLE
- You must have the entire unit circle memorized
- You should be able to state points, given angles, state angles given one of the
coordinates, know the value of all trig functions for any angle coterminal to one on the
unit circle etc. from memory without drawing the entire circle out.
APPLICATIONS
- s = r (theta)
-
right triangle applications. Understand angle of elevation and depression and be able to
set up the problems without a picture. REMEMBER angle of elevation/depression is
always measured from the horizontal (NOT VERTICAL)!
NOTE: you MUST have the UNIT CIRCLE and ALL ID’s MEMORIZED. They will not be given
on the test.
A few specific problems:
1. Given the angle 9 π /7
a) sketch the angle in standard position b) find 2 angles coterminal (one positive and one and
one negative) c) find the reference angle d) find the supplement of reference angle e) find the
complement of the reference angle f) convert to degrees g) convert to degrees, minutes seconds.
2. Given the angle -4.2
a) sketch the angle in standard position b) find 2 angles coterminal (one positive and one and one
negative) c) find the reference angle d) convert to degrees, minutes seconds.
3. Given tanθ = 5 and sec θ < 0, find the EXACT value of
a) sinθ b) csc(-θ) c) csc(π/2 – θ) d) cos(π+θ) e) sin(π/2-θ) f) tan(π-θ)
4. Evaluate EXACTLY a) cos(-13π/6) b) tan(2π/3) c) sin(31π/4) d) csc(-5π/6) e) cot(5π/3)
5 Find the reference angle for a) 4π/7 b) -3π/4 c) -15 d) 260º e) 5 f) 53π/6
6. Given (x, y) is on the unit circle in Quadrant II and y = 1/3. Find a) x b) cot (π/2-θ) c)sec θ
7. Given (2, -5) is on the terminal side of the angle θ. Find the EXACT value of all six trig
functions.
8. A meteor is making a circular orbit around Mars. If during the time the meteor travels 60,000
mi, it makes a central angle of 100º. What is the diameter of the orbit of this meteor?
9.A plane is traveling at an elevation of 5000 ft. The pilot sees 2 towns directly to the right of the
plane. If the first town is at an angle of depression of 20º and the second is at an angle of
depression of 35º, how far apart are the 2 towns? B) what of the second town was on the left
instead. How far apart would the towns be?
10. An airplane traveling at 10000 ft looks to the left and sees a church at an angle of depression
of 20º. The pilot sees a spaceship directly above the church at an angle of elevation 70º. How far
above the church is the spaceship? b) How far is the church from the point on the ground directly
below the airplane?
11. A pilot sees 2 towns to the left of his plane 2 towns are 30 miles apart. If the angle of
depression to 2 towns (both on the left) are 25º and 43º respectively, what is the elevation of the
plane? B) What is the second town was on the right? What would the elevation of the plane be?
12. A person standing 10 feet from a mirror notices that the angle of depression from his eyes to
the bottom of the mirror is 8° while the angle of elevation from his eyes to the top of the mirror is
12°. Find the height of the mirror.
13. A racing car travels in a circular motion around a judge’s stand. When the car travels
4800 feet, it has made a (central) angle of 120 at the judge’s stand. What is the diameter of
the track?
14.
How long should an escalator be if it is to make an angle of 21° with the floor and carry the
people a vertical distance of 27 feet between floors?
15. All applications from section 2.1 & 2.3 and lecture.
csc(10  )
 cos ( ) 
 cot 2 (80  ) completely. Show all work!
16. Simplify
2 


sec ( 5 )
cos(10 ) cot(10 )
1
2 3
10
Answers
1.b) -5π/7, 23π/7 c) 2π/7 d) 5π/7 e) 3π/14 f) 231.4286º g) 231º25’43”
2 a) (terminal side in QII) b) 2 π -4.2; -4.2-2 π c) 4.2 – π d) -240º30’32”
5 26
26
26
26
b)
c)  26 d)
e) 
f) -5
26
26
5
26
3
2
3
4. a)
db)  3 c) 
d) -2 e) 
2
2
3
5. a) 3π/7 b) π/4 c) 5π-15 d) 80º e) 2π-5 f) π/6
2 2
2
3 2
6. a) x  
b) 
c) 
3
4
4
5 29
2 29
5
29
29
2
;cos  
; tan    ; csc   
; sec  
; cot   
7. sin   
29
29
2
5
2
5
5
8.  
; r=34377.4677 mi; d = 68754.9354 mi
9
5000
5000
5000
5000

 6596.6471mi b)

 20878.1271mi
9. a)



tan 20
tan 35
tan 20
tan 35 
10000
10000
tan 70   85486.3217 ft b)
 27474.7742 ft
10. 10000 

tan 20
tan 20 
30 tan( 25  )
 27.9815mi
11.
25 )
1  tan(
tan(43 )
3. a) 
12. h=10tan(12°) + 10tan(8°) = 3.5310 ft
13. r 
14.
d
16. 2
7022

 2291.8312 ft
27
 75.3416 ft
sin( 21 )