Sum and Difference Formulas New Identities Cosine Formulas

Sum and Difference Formulas New Identities

Cosine Formulas

Sine Formulas

Tangent Formulas

Using Sum Formulas to Find Exact Values n n n Find the exact value of cos 75 o = cos (30 o + 45 o) cos 30 o cos 45 o – sin 30 o sin 45 o

Find the Exact Value n Find the exact value of

Exact Value n Find the exact value of tan 195 o

Using Difference Formula to Find Exact Values n Find the exact value of sin 80 o cos 20 o – sin 20 o cos 80 o n This is the sin difference identity so. . . n sin(80 o – 20 o) = sin (60 o) = n

Using Difference Formula to Find Exact Values n Find the exact value of n cos 70 o cos 20 o – sin 70 o sin 20 o n This is just the cos difference formula n cos (70 o + 20 o) = cos (90 o) = 0

Finding Exact Values

Establishing an Identity n Establish the identity:

Establishing an Identity n Establish the identity n cos (a + b) + cos (a – b) = 2 cos a cos b

Solution n n cos (a + b) + cos (a – b) = 2 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

Establishing an Identity n n Prove the identity: tan (q + p) = tan q

Solution

Establishing an Identity n Prove the identity:

Solution

Finding Exact Values Involving Inverse Trig Functions n Find the exact value of:

Solution n n 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 1 st quadrant and b is in the 4 th quadrant (remember range)

Solution

Solution

Writing a Trig Expression as an Algebraic Expression n Write sin (sin-1 u + cos-1 v) 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 n n Let sin-1 u = a and cos-1 v = b Then sin a = u and cos b = v

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