SOLUTION: How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a − b) if cos a = 4/5 tan a < 0, tan b = −√15 and cos b < 0
cos(a-b) =
Algebra.Com
Question 925555: How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a − b) if cos a = 4/5 tan a < 0, tan b = −√15 and cos b < 0
cos(a-b) =
and
Evaluate sin(x + y) if sin x = 3/5 sec x > 0, cos y = − (2√5)/5 and tan y < 0.
sin(x + y) =
THANKS!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
evaluate these this two sine and cosine problems. Difficult!?
Evaluate::
cos(a − b) if cos a = 4/5 tan a < 0,
Note:: a is in QII where x is positive and y is negative
Since cos = x/r, x = 4 and y = -sqrt(5^2-4^2) = -3
Then sin(a) = y/r = -3/4
------------------
tan b = −√15 and cos b < 0
Note:: b is in QII where x is negative and y is positive
Since tan = y/x, y = sqrt(15) and x = -1
Then sin(b) = y/r = sqrt(15)/sqrt((sqrt(15))^2+1^2) = sqrt(15)/4
and cos(b) = x/r = -1/4
---------------------------------------------
cos(a-b) = cos(a)cos(b)+sin(a)sin(b)
----
= (4/5)*(-1/4) + (-3/4)(sqrt(15)/4)
=====================================
and
Evaluate sin(x + y) if sin x = 3/5 sec x > 0, cos y = − (2√5)/5 and tan y < 0.
sin(x + y) =
---Whoops:: Got to run. Maybe you can finish this now.
Cheers,
Stan H.
------------
RELATED QUESTIONS
How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a... (answered by richard1234)
How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a... (answered by lwsshak3)
Evaluate without using a calculator.
sin θ, if cos θ = 2/5 and tan θ < 0. (answered by lwsshak3)
if tan A = 4/3 and tan B=12/5.find cos (A-B)
given 0<... (answered by Fombitz)
if tan A = 4/3 and tan B=12/5. find cos (A-B)
given 0< A < B <... (answered by Theo)
If tanα =4/3 and cosβ = 12/13, where 0<β<α<90°, evaluate without... (answered by lwsshak3)
im completely lost on how to work these out,
Given cos A =0.42 and sin B = 0.73... (answered by jsmallt9)
if tan a and tan b are the roots of equation 4x^2-7x+1=0 then evaluate... (answered by ikleyn)
if tan A = 4/3 and tan B=12/5.find cos (A-B)
(answered by Fombitz)