Pre-Calculus
Lecture 4.4
Name_________________
Let θ be an angle in standard position with (x,y), a point on the terminal side of the
angle and
r=
x2 + y2 ! 0
y
x
cos" =
r
r
r
csc" = y ! 0 sec" =
y
sin" =
y
tan" = x ! 0
x
r
x
x ! 0 cot" = y ! 0
x
y
Note: If x = 0, then Tan θ and Sec θ are undefined.
If y = 0, then Cot θ and Csc θ are undefined.
Let (-5, 12) be a point on the terminal side of θ. Find all six trig ratios.
Quadrant 1
Sine & Cosecant
Cosine & Secant
Tangent & Cotangent
Quadrant 2
Quadrant 3
Quadrant 4
Given: Tan θ = -4/5 and cos θ > 0. Find the remaining trig ratios.
Fill in the following chart:
Sin θ
π/2
π
3π/2
2π or 0
Cos θ
Tan θ
Cot θ
Sec θ
Csc θ
Reference Angle: Let θ be an angle in standard position. It’s reference angle is the acute
angle θ’ formed by the terminal side of θ and the horizontal axis.
Find the reference angle for each of these:
a) 130°
b) 210°
c) 315°
d) 4π/3
e) 4π/5
f) 11π/6
In which quadrants are the trig ratios positive?
Evaluate the trigonometric functions for each of the following: (exact answers only)
a) Cos 4π/3
b) Tan (-210°)
c) sec 11π/4
Let θ be an angle in Quadrant II such that Sin θ = 1/3. Using trig identities, find the following:
a) Cos θ
b) Tan θ
Use your calculator to evaluate each of the following: Round values to four decimal places:
a) Tan (-210°)
b) Cos 132°
d) Tan (4π/3)
e) Sin (12π/7)
c) Csc (-235°)
f) Sec (15π/4)
Use your calculator to find two approximate values of θ (0° ≤ θ ≤ 360°). Round your
answers to two decimal places.
a) Cos θ = 0.6820
b) Sin θ = 0.7880
Find the indicated trigonometric value in the specified quadrant:
a) Csc θ = -2, Quadrant IV, find Cot θ.
b) Sec θ = -9/4, Quadrant III, find Tan θ.
c) Tan θ = 0.8693