Trigonometric
relationships
IB SL/HL
Adrian Sparrow
www.ibmaths.com
Simplify the following:
1.
2.
3.
4.
5.
Consider the circle shown
The Unit Circle - tan opposite.
y
Make a right angled triangle.
(x,y)
An expression for x:
1
y
x
x
An expression for y:
And now use tan:
The Unit Circle - Make a right angled triangle.
Pythagoras
Make up an equation using
Pythagoras:
Put your GDC into radian mode,
set the window at and
.
Draw the graph .
Draw the graph on the
same axis.
What do you notice?
Draw the graph of
on the same axis.
Important note:
Using these relationships There are 2 possible answers for
cosx. As x is obtuse, the angle is in
the 2nd quadrant so,
b) Use:
1. Given that and x is
obtuse, find,
a) cosx
b) tanx
a) Use:
Check this with your trig. ratios
table.
Using these relationships 4cos2 x 3cosx 2 0
This is a quadratic equation.
Use the equation solver on your
GDC:
1. Solve x in the following
equation,
Use cosx=1.175 (not possible)
Use a relationship such that the
equation is all cosx or all sinx. Use cosx=-0.4253
x=116o and 244o
1. Given that and is 4. Given that and is
acute, find, negative, find,
a) b) a) b)
2. Find the value of x in the 5. Find the value of x in the
equation, equation,
3. Find the value of in the
equation,
1. Given that and is 4. Given that and is
acute, find, negative, find,
a) b) a) b)
2. Find the value of x in the 5. Find the value of x in the
equation, equation,
3. Find the value of in the
equation,