Chapter 4.2
Trigonometric Functions of Acute Angles.
Learning Targets: I can define the six
trigonometric functions using lengths of the sides
of a right triangle.
Trig Functions
Let θ be an acute angle in the right Δ, then
•
•
•
•
•
•
•
Sine (θ) = sin θ = opp/hyp
Cosine (θ) = cos θ = adj/hyp
Tangent (θ) = tan θ = opp/adj
(Remember Soh Cah Toa)
Cosecant (θ) = csc θ = hyp/opp
Secant (θ) = sec θ = hyp/adj
Cotangent (θ) = cot θ = adj/opp
Recall from Geometry
• 30-60-90 triangle and 45-45-90 triangle
• Do you remember their side ratios?
Quick Note
• On your calculators, the tan-1, sin-1, and
cos-1 are not the same as cot, csc, and
sec. -1 represents the inverse, not the
reciprocal.
Example
• Solve the right triangle.
11
b
28°
a
Example
• A right triangle with a hypotenuse of 8
includes a 37° angle. Find the measure of
the other two angles and the lengths of the
other two sides.
Example
• Find the value of all six trig functions of
angle θ.
17
8
15
Example
• Assume that θ is an acute angle in a right
triangle satisfying the given conditions.
Evaluate the remaining 5 trig functions.
• Sin θ = 2/3
Example
• Evaluate using a calculator.
• Tan (8°) =
• Sin (Π/15) =
Example
• Solve for the variable shown.
14
x
43°
Homework
Pg. 366
# 1 – 17 odd, 29 – 39 odd, 49 – 57 odd