Download Trigonometry 2 - Trig Ratios_1

Math 10C
Trigonometry Lesson #2
Trigonometric Ratios
Objective: By the end of this lesson you will be able to:
We have seen that the ratios of the side lengths of any right triangle with a given acute angle are
always ____________________.
Since the ratios between the sides will always be the same for any right triangle with a specified
angle, we give a name to the ratios between the sides:
Primary Trigonometric Ratios:
opposite

adjacent
opposite

hypotenuse
adjacent

hypotenuse
The primary trig ratios can be memorized using the acronym
e.g. 1) Find the tangent, sine, and cosine ratios for X in the triangle below. Express your
answers as fractions in lowest terms.
X
5 cm
Y
Z
12 cm
We can use a calculator to give us the value of the primary trig ratios if we know the measure of
the angle. These will often be ___________________ numbers.
Math 10C
Trigonometry Lesson #2
Important: Make sure your calculator is in degree mode for this unit!
e.g. 2) Use your calculator to find the value of the following trig ratios to 4 decimal places.
a) sin 15
This means that any for any right triangle with a ______ angle, the ratio of the
_________________ side to the __________________ will be ____________.
b) tan 68
This means that any for any right triangle with a ______ angle, the ratio of the
_________________ side to the _______________ side will be ____________.
c) cos 60
This means that any for any right triangle with a ______ angle, the ratio of the
_________________ side to the __________________ will be ____________.
e.g. 5) Use a ruler to draw a right triangle BCD such that C  90 and tan D 
7
.
3
a) Find tan B of the triangle. How does it compare to tan D ?
b) Find the length of the hypotenuse of BCD . Leave your answer as a square root.
c) Find sin B and cos D . What do you notice? Why is this the case?
Math 10C
Trigonometry Lesson #2
e.g. 4) Sketch an isosceles right triangle and use it to explain why tan 45  1 .
Assignment:
p. 75-77 #3, 6, 7, 16 (For a challenge: #23)
p. 94-96 #3-5, 9, 15, 16