Download Trig Identities The ones you already know: 1 + cot θ = csc

April 03, 2011
Trig Identities
The ones you already know:
NEW: PYTHAGOREAN IDENTITIES
2
· What would sin θ equal?
sin2θ = 1 - cos2θ
2
· What would cos θ equal?
cos2θ = 1 - sin2θ
2. Let's take 2the original Pythagorean identity and
divide by sin θ. What is the new identity that we get?
1 + cot2θ = csc2θ
3. Let's take the
original Pythagorean identity and
2
divide by cos θ. What is the new identity that we get?
tan2θ + 1 = sec2θ
April 03, 2011
Examples:
HINT
1. Simplify: cotθsecθ in terms of sinθ
First: Find an identity to substitute a
different function for one of the given
functions. (You want to try and get
them all to be the same trig function.)
2. Simplify the expression
trigonometric function.
to a single
3. Simplify:
4. Write this expression as a monomial with a single
trigonometric function:
April 03, 2011
5. Simplify the expression:
Practice: Write the expression as a
monomial containing a single function
7. sinθsecθ
6. sinθcotθ
9. secθsinθcscθ
8. secθcotθsinθ
2
2
11. sinθ(cot θ + 1)
10. cscθ(1 - cos θ)
2
12. secθcosθ - cos θ
Using Identities in Equation Solving:
If there is more than one trig function in the equation,
identities are needed to reduce the equation to a single
function for solving.
2
1. Solve: 2cos x + 3sinx - 3 = 0
Use the Pythagorean Identities
to replace the squared term!
2
2. 2cos x - sinx = 1
2
3. sec x - tanx - 1 = 0
4. cosx = secx
5. 2sinx = cscx
April 03, 2011