This document discusses trigonometric ratios and the unit circle. It explains that for any point (x,y) on the unit circle, x=cosθ and y=sinθ. It also reviews trig ratio definitions and relationships like tangent=sin/cos. The document provides examples of finding trig function values given other information about a point on the unit circle. It introduces cosecant, secant and cotangent as reciprocal trig functions and confirms the CAST rule applies to them as well.
The programme explains the concept of trigonometry.It also attempts to explain various parts of a right angled triangle -hypotenuse,adjacent side and opposite sides.It also gives the explanation of trigonometric ratios-sine,cosine and tangents.
The programme explains the concept of trigonometry.It also attempts to explain various parts of a right angled triangle -hypotenuse,adjacent side and opposite sides.It also gives the explanation of trigonometric ratios-sine,cosine and tangents.
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Review of Trigonometry for Calculus “Trigon” =triangle +“metry”=measurement =...KyungKoh2
Review of Trigonometry for Calculus “Trigon” =triangle +“metry”=measurement =Trigonometry so Trigonometry got its name as the science of measuring triangles.
1. What do you call the acute angle formed by the terminal side o.docxdorishigh
1. What do you call the acute angle formed by the terminal side of an angle θ in standard position and the horizontal axis?
complementarysupplementary coterminalquadrantreference
2. In which quadrants is sin θ positive? (Select all that apply.)
Quadrant IQuadrant IIQuadrant IIIQuadrant IV
3. For which of the quadrant angles 0, π/2, π, and 3π/2 is the cos function equal to 0? (Select all that apply.)
0π/2π3π/2
4. Is the value of cos 165° equal to the value of cos 15°?
YesNo
5. Determine the exact values of the six trigonometric functions of the angle θ.
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
6. Determine the exact values of the six trigonometric functions of the angle θ.
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
7. Determine the exact values of the six trigonometric functions of the angle θ.
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
8. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.
(−80, 18)
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
9. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.
(–7, –8)
sin(θ)
=
cos(θ)
=
tan(θ)
=
csc(θ)
=
sec(θ)
=
cot(θ)
=
10. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.
(5, −8)
sin(θ)
=
cos(θ)
=
tan(θ)
=
csc(θ)
=
sec(θ)
=
cot(θ)
=
11. State the quadrant in which θ lies.
sec θ > 0 and cot θ < 0
III IIIIV
12. State the quadrant in which θ lies.
tan θ > 0 and csc θ < 0
III IIIIV
13. Find the values of the six trigonometric functions of θ with the given constraint. (If an answer is undefined, enter UNDEFINED.)
Function Value
Constraint
csc θ = 6
cot θ < 0
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
14. Find the values of the six trigonometric functions of θ with the given constraint. (If an answer is undefined, enter UNDEFINED.)
Function Value
Constraint
tan θ is undefined.
π ≤ θ ≤ 2π
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
15. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
sec π
16. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
csc 0
17. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
csc
3π
2
18. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
csc
7π
2
19. Find the reference angle θ' for the special angle θ.
θ = −295°
θ' = °
Sketch θ in standard position and label θ'.
20. Find the reference angle θ' for the special angle θ. (Round your answer to four decimal places.)
θ =
2π
3
θ' =
Sketch θ ...
This lesson is the second of the series I am working on. It really should have come first, though. This lesson introduces trigonometry, detailing what it is, what is uses and a few important topics and formulas you'll find yourself using quite frequently.
with today's advanced technology like photoshop, paint etc. we need to understand some basic concepts like how they are cropping the image , tilt the image etc.
In our presentation you will find basic introduction of 2D transformation.
1. Trig Ratios & Unit Circle
Using Pyth
On unit circle
This is true for
on the unit circle
2. Coordinates of Points on Unit Circle
cos =x=x=x
=y=y=y
r 1
Conclusion: For all points on the unit circle, since
r = 1, we can replace cos with x and sin with y
3. ) represent any point on the unit circle
and has the coordinates (cos , sin )
SO, P( ) = (cos , sin )
How about, tan = y = sin
x cos
4. This is summarized in CAST rule
In which quadrant does the terminal arm of lie if:
a) sin < 0 and tan > 0
b) cos < 0 and tan < 0
5. Finding P( ) on Unit Circle
If given a point with coordinates (5, 12),
how do you find the corresponding point
on the unit circle, ie, P( ) ?
If sin = and cos =
Find tan
6. If cos = , find sin
Given sin = and tan < 0, find cos.
7. 3 New Reciprocal Trig
Ratios or Functions
= sec = 1 = 1 = r
cos x x
r
cosecant = csc = 1 = 1 = r
sin y y
r
cotangent = cot = cos
CAST still applies
Give 6 trig ratios over (0, ) if sin = 3
5