Home > Trigonometry > Sum and Difference Identities

How do you find the exact functional value tan 7pi/12 using the cosine sum or difference identity?

Answer 1

Find #tan ((7pi)/12)#

Ans: #(1 + sqrt3)/(1 - sqrt3)#

#sin ((7pi)/12) = sin (pi/3 + pi/4) =# #= sin (pi/3).cos (pi/4) + sin (pi/4).cos (pi/3) =# #(sqrt3/2)(sqrt2/2) + (sqrt2/2)(1/2) = ((sqrt2)/4)(1 + sqrt3)# #cos ((7pi)/12) = cos (pi/3 + pi/4) = # #= cos (pi/3).cos (pi/4) - sin (pi/3).sin (pi/4) =# #= (1/2)(sqrt2/2) - (sqrt2/2)(sqrt3/2) = (sqrt2/4)(1 - sqrt3)#

#tan ((7pi)/12) = sin/(cos) = (1 + sqrt3)/(1 - sqrt3)# Check by calculator: #tan ((7pi)/12) = tan 105 = -3.73# #(1 + sqrt3)/(1 - sqr3) = 2.73/(-0.73) = - 3.73#. OK

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Asher Friedman

To find the exact functional value of tan(7π/12) using the cosine sum or difference identity, you can first express tan(7π/12) in terms of sine and cosine using the identity tan(θ) = sin(θ) / cos(θ). Then, you can use the angle addition formula for cosine, which states that cos(A + B) = cos(A)cos(B) - sin(A)sin(B), where A = 3π/4 and B = π/3. After substituting the values, simplify the expression to find the exact value of tan(7π/12).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.