Tool: Verifying trig identities (see p. 441). An
identity is an equation that should be true for all values of θ . If it is, then
you can use the identities you already know to simplify both
sides to be equal to each other.
Tool: If we set u=v=θ in the sum angle formulas, we
obtain the double angle formulas. Note that double angle
formula for cosine has a couple of equivalent forms based on
the Pythagorean identity.
Tool: Half angle identities. These are derived from
double angle cosine identities and replacing θ by θ/2
(see p. 462).
4 Trig Equations
Tool: Trig equations are true only for certain
values of an
angle ( unlike identities , which are true for all values).
Always be aware of restrictions. They will tell you where to
look for solutions when you apply inverse trig functions.
Tool: Trig identities can be used to solve. You may
Simplifying trig expressions:
Verifying Trig identities for all angular values:
Proving an equation is not an identitiy:
Practice with cosine sum and difference formulas:
Compute the fol lowing exactly (no decimal).
Cofunction identity practice:
What is sec(90−θ)?
Evaluate the expression exactly (no decimal): Hint: recognize the proper identity to simplify
Evaluate the expression exactly (no decimal):
Hint: inverse trig functions output angles. Use triangles
find those angles.
(optional)Practice: You don't really need to
of sum and difference angle formulas because you can use
even-odd properties to derive one from the other.
Derive the formula for tan(u+v) using even-odd
identities for tangent.
Evaluating trig functions.
Let θ be a first quadrant angle such that tan(θ)= 5/12 .
Compute exactly (no decimal).
Start solving your Algebra Problems
in next 5 minutes!
Download (and optional CD)
Click to Buy Now:
2Checkout.com is an authorized reseller
of goods provided by Sofmath
Attention: We are
currently running a special promotional offer
for Algebra-Answer.com visitors -- if you order
Algebra Helper by midnight of
you will pay only $39.99
instead of our regular price of $74.99 -- this is $35 in
savings ! In order to take advantage of this
offer, you need to order by clicking on one of
the buttons on the left, not through our regular
If you order now you will also receive 30 minute live session from tutor.com for a 1$!
You Will Learn Algebra Better - Guaranteed!
Just take a look how incredibly simple Algebra Helper is:
: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:
Step 2 :
Let Algebra Helper solve it:
Step 3 : Ask for an explanation for the steps you don't understand:
Algebra Helper can solve problems in all the following areas:
simplification of algebraic expressions (operations
with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots
(radicals), absolute values)