240 likes | 492 Views
Sum and Difference Formulas. New Identities. Cosine Formulas. Sine Formulas. Tangent Formulas. Using Sum Formulas to Find Exact Values. Find the exact value of cos 75 o cos 75 o = cos (30 o + 45 o ) cos 30 o cos 45 o – sin 30 o sin 45 o. Find the Exact Value. Find the exact value of.
E N D
Sum and Difference Formulas New Identities
Using Sum Formulas to Find Exact Values • Find the exact value of cos 75o • cos 75o = cos (30o + 45o) • cos 30o cos 45o – sin 30o sin 45o
Find the Exact Value • Find the exact value of
Exact Value • Find the exact value of tan 195o
Using Difference Formula to Find Exact Values • Find the exact value of • sin 80o cos 20o – sin 20o cos 80o • This is the sin difference identity so . . . • sin(80o – 20o) = sin (60o) =
Using Difference Formula to Find Exact Values • Find the exact value of • cos 70o cos 20o – sin 70o sin 20o • This is just the cos difference formula • cos (70o + 20o) = cos (90o) = 0
Establishing an Identity • Establish the identity:
Establishing an Identity • Establish the identity • cos (a + b) + cos (a – b) = 2 cos a cos b
Solution • cos (a + b) + cos (a – b) = 2 cos a cos b • cos a cos b –sin a sin b + cos a cos b + sin a sin b • cos a cos b + cos a cos b = 2 cos a cos b • 2 cos a cos b = 2 cos a cos b
Establishing an Identity • Prove the identity: • tan (q + p) = tan q
Establishing an Identity • Prove the identity:
Finding Exact Values Involving Inverse Trig Functions • Find the exact value of:
Solution • Think of this equation as the cos (a + b) (Remember that the answer to an inverse trig question is an angle). • So . . . a is in the 1st quadrant and b is in the 4th quadrant (remember range)
Writing a Trig Expression as an Algebraic Expression • Write sin (sin-1u + cos-1v) as an algebraic expression containing u and v (without any trigonometric functions) • Again, remember that this is just a sum formula • sin (a + b) = sin a cos b + sin b cos a
Solution • Let sin-1u = a and cos-1v = b • Then sin a = u and cos b = v
On-line Help • Tutorials • Videos