Angles in Quadrant 1 (6.1 )
The Point P (1,8) lies on the terminal arm of an angle θ in standard position.
Find tanθ .
8/1=8
In what quadrants is the Sine of an angle positive?
Quadrants I and II
The point P(-1, -3) lies on the terminal arm of an angle θ in standard position.
Find sinθ .
sinθ=-3/sqrt(10)
Given a reference angle θ =47 degrees, what other angles have the same reference angle?
133, 227, and 313 degrees
To the nearest degree, what angles between 0 and 360 satisfy the following trigonometric equation?
sinθ=-1
270 degrees
The point (3, 12) lies on the terminal arm of an angle in standard position. Determine the primary trigonometric ratios of θ .
cosθ=3/sqrt(153)
tanθ=12/3=4
sinθ=12/sqrt(153)
All Silver Tea Cups
All in Quadrant I
Sine in Quadrant II
Tangent in Quadrant III
Cosine in Quadrant IV
The point P(4,-27) lies on the terminal arm of an angle θ in standard position.
Determine the primary trigonometric ratios of θ.
sinθ=-27/sqrt(745)
cosθ=4/sqrt(745)
tanθ=-27/4
Given an angle θ=221 degrees, what is this angle's reference angle?
41 degrees
To the nearest degree, what angles between 0 and 360 satisfy the following trigonometric equation?
cosθ=0
90 and 270 degrees
The point (5, 17) lies on the terminal arm of an angle θ in standard position. Determine the primary trigonometric ratios of θ AND find θ to the nearest degree.
sinθ=17/sqrt(314)
cosθ=5/sqrt(314)
tanθ=17/5
θ is about 74 degrees.
When finding the reference angle given the following trig ratio, what should we type into the calculator and why?
sinθ=(-5/6)
sin^-1(5/6)
We do this because reference angles are in quadrant I and all trig ratios are positive in quadrant I.
The point (-4, 9) lies on the terminal arm of an angle θ in standard position.
What Quadrant is θ in?
Determine the measure of θ to the nearest degree.
Quadrant II
θ is about 114 degrees.
Given an angle θ =345 degrees, what other angles use the same reference angle?
Reference angle=15 degrees
Other angles=165 and 195 degrees
To the nearest degree, what angles between 0 and 360 satisfy the following trigonometric equation?
cosθ=-9/28
109 and 251 degrees
The following angle θ is in standard position in Quadrant 1. Find cosθ and tanθ given sinθ below.
sinθ=4/sqrt(17)
tanθ=4/1=4
cosθ=1/sqrt(17)
If you know the primary trig ratios of an angle in any quadrant, how many other angles do you know the trig ratios for?
What is the only thing that changes between these angles.
Three, one in each of the other three quadrants.
The signs of the sine, cosine, and tangent change between positive and negative depending on what quadrant it is in.
The point P(-5, -8) lies on the terminal arm of an angle θ in standard position.
What is the angle to the nearest degree?
238 degrees
The terminal arm of an angle A lies in Quadrant 3, cosθ=2/9 (θ is reference angle). What is sinA?
Find A to the nearest degree.
sinA=-sqrt(77)/9
A=257 degrees
To the nearest degree, what angles between 0 and 360 satisfy the following trigonometric equation?
sinθ=100/101
82 and 98 degrees
Point P is on the terminal arm of an angle in standard position in Quadrant 1. The distance r between P and origin is given. Determine the possible coordinates for P.
r=sqrt(57)
Answers may vary.
x^2+y^2=57
Given a reference angle θ in Quadrant I, how do you find the angles that use the same reference angle in the other three quadrants?
Quadrant II: 180-θ
Quadrant III: 180+θ
Quadrant IV: 360-θ
The point P(-59, 112) lies on the terminal arm of an angle θ in standard position.
Determine the angle to the nearest degree.
118 degrees
The terminal arm of an angle A lies in Quadrant 4, cosθ=3/8 (θ is reference angle). What is tanA?
Find A to the nearest degree.
tanA=-sqrt(55)/3
A=292 degrees
To the nearest degree, what angles between 0 and 360 satisfy the following trigonometric equation?
tanθ=-.05
177 and 357 degrees.